Kyushu University Academic Staff Educational and Research Activities Database
List of Presentations
Yoshio Ebihara Last modified date:2022.05.02

Professor / Department of Electrical Engineering / Faculty of Information Science and Electrical Engineering


Presentations
1. Y. Ebihara, L1-induced Norm Analysis of Positive Systems and Its Application, Kolloquium Technische Kybernetik, The University of Sttutgart, 2019.09.
2. Y. Ebihara, N. Sebe, H. Waki, On Gain-Scheduled State-Feedback Controllers Synthesis under Quadratic Stability Condition, Conference on Decision and Control, 2020.12.
3. Y. Ebihara, D. Peaucelle, D. Arzelier, The Hankel-type Lq/Lp Induced Norms of Positive Systems Across Switching, European Control Conference, 2020.07.
4. Yoshio Ebihara, Patrizio Colaneri, Jose C. Geromel, H2 state-feedback control for continuous-time systems under positivity constraint, 18th European Control Conference, ECC 2019, 2019.06, This study is concerned with the H{2} state-feedback controller synthesis problem under positivity constraint on the closed-loop system. This problem is believed to be a nonconvex problem in both continuous-and discrete-time system settings and hence remains to be the most challenging issue in positive system theory. For this hard problem, in the discrete-time system setting, the authors recently proposed a technique for the lower bound computation of the best achievable H{2} performance by a specific treatment of finite impulse responses (FIRs) of the closed-loop systems. The goal of this paper is to extend this idea to the continuous-time system setting. Even though there is no notion of FIR in (finite-dimensional) continuous-time system impulse responses, the truncation of the Taylor series expansion of the matrix exponential function in the impulse response paves the way for obtaining a semidefinite programming problem (SDP) for the lower bound computation. We show that, by increasing the truncation degree, we can construct a sequence of SDPs that generates a monotonically non-decreasing sequence of the lower bounds. By combining this lower bound computation technique with heuristic upper bound and suboptimal gain computation techniques, it becomes possible to draw definite conclusion on the quality of the computed suboptimal gains..
5. Yoshio Ebihara, H2 State-Feedback Synthesis under Positivity Constraint
Upper and Lower Bounds Computation of the Achievable Performance, 16th European Control Conference, ECC 2018, 2018.11, This paper is concerned with the H-{2} state- feedback synthesis problem under positivity constraint on the closed-loop system. This problem is believed to be a non-convex problem and hence exact treatment is not known to this date. With this difficulty in mind, in this paper, we first derive several semidefinite programs (SDPs) for the computation of the upper bounds of the achievable performance as well as suboptimal gains. However, if we rely only on the upper bound computation, we cannot say anything quantitatively on the quality of the computed suboptimal gains. For such quantitative evaluation, we next derive an SDP for the lower bound computation of the achievable performance. The key idea in deriving such an SDP is that, if the closed-loop system is positive, then the Lya- punov variable in the standard SDP for the H-{2} state-feedback synthesis should be (elementwise) nonnegative. By numerical examples, we illustrate the effectiveness and limitation of the proposed strategy with upper and lower bounds computation. Keywords: H-{2} state-Feedback synthesis, positivity constraint, upper and lower bound computation..
6. Yoshio Ebihara, Linear-Programming-Based Decentralized Stabilizing Controller Synthesis for Interconnected Positive Systems and its Optimality Property, 57th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2018, 2018.10, This study is concerned with decentralized stabilizing controller synthesis problem for interconnected systems constructed from positive subsystems. The main issue is how to design a controller for each subsystem locally so that positivity and stability of the overall interconnected system can be attained. Under a specific interconnection structure, the author has already shown that such a controller can be designed locally without any information about the rest of the positive subsystems. Namely, under the specific interconnection structure, we can reduce the original problem into a set of L-1- induced-norm optimal controller synthesis problems for subsystems each of which can be solved indeed locally via linear programming. On the basis of these preceding results, in this study, we show an optimality property of such local L-1 -induced-norm optimal controllers in a global sense. More precisely, we prove that the set of L-1 -induced-norm optimal controllers is indeed globally optimal in the sense that it minimizes the abscissa of the coefficient matrix of the overall interconnected closed-loop system..
7. Yoshio Ebihara, Patrizio Colanoli, Jose C. Geromel, H2 state-feedback synthesis for discrete-time systems under positivity constraint, 2018 SICE International Symposium on Control Systems, SICE ISCS 2018, 2018.04, This paper is concerned with the H2 state-feedback synthesis problem for discrete-time systems under positivity constraint on the closed-loop systems. This problem is believed to be a non-convex problem and hence exact treatment is not known to this date. With this difficulty in mind, in this paper, we first derive semidefinite programs (SDPs) for the computation of the upper bounds of the achievable H2 performance as well as suboptimal gains. However, if we merely rely on the upper bound computation, we cannot draw any definite conclusion on the quality of the computed suboptimal gains. Thus the main issue of the present paper is the lower bound computation, and to this end we derive an SDP for that computation via specific treatment of the finite impulse resonse (FIR) with the idea of time-varying gain synthesis. We show that the lower bounds become tighter as we increase the length of the FIR. By numerical examples we show the soundness of the proposed strategy with upper and lower bounds computation..
8. Yoshio Ebihara, Dominant pole analysis of neutral-type time delay positive systems, 56th IEEE Annual Conference on Decision and Control, CDC 2017, 2018.01, This paper is concerned with dominant pole analysis of neutral-type time delay positive systems (TDPSs). The neutral-type TDPS of interest is constructed by feedback connection between a finite-dimensional linear time-invariant positive system (FDLTIPS) and the pure delay, where the FDLTIPS has a nonzero direct feedthrough term. It has been shown very recently that this neutral-type TDPS is asymptotically stable if and only if its delay-free finite-dimensional counterpart is stable and admissible, where the latter means that the direct feedthrough term is Schur stable. This result in particular implies that the stability is irrelevant of the length of the delay. However, it is strongly expected that convergence or divergence rate depends on the delay length and this is the motivation for the dominant pole analysis. In this paper, we show that one of the dominant poles of the neutral-type TDPS is real irrespective of the stability, and we derive closed-form formulas that relate the real dominant pole with the delay length for both stable and unstable neutral-type TDPSs..
9. Yoshio Ebihara, Hz analysis of LTI systems via conversion to positive systems, 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017, 2017.11, Motivated by recent drastic advances in the study of linear-time invariant (ETI) positive systems, we explore analysis techniques of general, not necessarily positive ETI systems using positive system theory. Even though a positive system is characterized by its peculiar property that its impulse response is nonnegative, we often deal with nonnegative impulse responses even in general ETI system analysis. A typical example is the computation of the H2 norm where we focus on squared impulse responses. To deal with such products of impulse responses in a systematic fashion, in this paper, we first establish a construction technique of an ETI system whose impulse response is given by the product of impulse responses of two different ETI systems. Then, as the main result, we reduce the H2 norm computation problem of a general ETI system into the L-induced norm computation problem (or L1 problem in short) of a positive system, by which we can derive a closed-form formula for the H norm computation..
10. Yoshio Ebihara, Naoya Nishio, Tomomichi Hagiwara, Stability analysis of neutral type time-delay positive systems, 5th International Symposium on Positive Systems, POSTA 2016, 2017.01, This chapter is concerned with asymptotic stability analysis of neutral type time-delay positive systems (TDPSs). We focus on a neutral type TDPS represented by a feedback system constructed from a finite-dimensional LTI positive system and the pure delay, and give a necessary and sufficient condition for the stability. In the case where we deal with a retarded type TDPS, i.e., if the direct-feedthrough term of the finite-dimensional LTI positive system is zero, it is well known that the retarded type TDPS is stable if and only if its delay-free finite-dimensional counterpart is stable. In the case of neutral type TDPS, i.e., if the direct-feedthrough term is nonzero, however, we clarify that the neutral type TDPS is stable if and only if its delay-free finite-dimensional counterpart is stable and the direct-feedthrough term is Schur stable. Namely, we need additional condition on the direct-feedthrough term..
11. Hayato Waki, Yoshio Ebihara, Noboru Sebe, Reduction of SDPs in H control of SISO systems and performance limitations analysis, 55th IEEE Conference on Decision and Control, CDC 2016, 2016.12, In SDP-based H control, we often encounter numerical difficulties when solving SDPs by various pieces of software. It is empirically known that such numerical difficulty occurs if an SDP at hand or its dual has no interior point feasible solutions, and this is indeed the case of some SDPs in H control. To conceive a way for getting around such numerical difficulties in a concrete problem setting, in this paper, we focus on the dual SDP for the H control problem of the transfer function (1 + PK)-1P and simplify it. More precisely, by actively using the information of unstable zeros (non-minimum phase zeros) of the plant P, we reduce the original dual SDP into a set of simplified SDPs each of which and its dual have interior point feasible solutions. In this way, we show by numerical experiments that reliable numerical computation can be done by SDP software. On the other hand, once we have obtained simplified SDPs, it becomes possible to further reduce them into the computation of maximum singular values of matrices determined by unstable zeros. In this way, if the number of unstable zeros is moderate, we can obtain analytical expressions of the best achievable H performance or its lower bounds in terms of the unstable zeros. Keywords: H control, SDP, numerical reliability, best achievable performance..
12. Yoshio Ebihara, Hayato Waki, Noboru Sebe, Dual LMI approach to H performance limitation analysis of sensitivity and complementary sensitivity functions, 2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016, 2016.10, In this paper, we study a dual-LMI-based approach to H performance limitation analysis of SISO systems. The scope includes the analysis of the sensitivity function S = (1 + PK)-1 and the complementary sensitivity function T = (1 + PK)-1 PK where P and K stand for the plant and the controller, respectively. The H performance limitations for these transfer functions are well investigated, and exact closed-form performance bounds are already known for the cases where the plant has the sole unstable zero (i.e., non-minimum phase zero) of degree one or the sole unstable pole of degree one. The goal of this paper is to show that such exact bounds can be reproduced by a dual LMI approach. To this end, we study a Lagrange dual of the standard SDP that is usually used to design H optimal controllers by numerical computation. By characterizing the structure of dual feasible solutions in terms of unstable zeros and unstable poles of the plant, we clarify that we can construct an optimal solution for the dual SDP analytically. It follows that we obtain exact H performance bounds that are consistent with the known results..
13. Yoshio Ebihara, Shogo Shintani, Tomomichi Hagiwara, Dual LMI approach to H∞ performance limitations analysis of SISO systems with multiple unstable zeros and poles, 2016 American Control Conference, ACC 2016, 2016.07, In this paper, we study a dual-LMI-based approach to H∞ performance limitations analysis of SISO systems with multiple (i.e., duplicated) unstable zeros and poles. The scope includes the analysis of the transfer functions M = (1+PK)-1 P, S = (1+PK)-1, and T = (1+PK)-1 PK where P and K stand for the plant and the controller, respectively. The latter two transfer functions are well investigated, and exact closed-form performance bounds are already known for the cases where the plant has the sole unstable zero of degree one or the sole unstable pole of degree one. However, such exact bounds are hardly available for the cases where the plant has multiple (i.e., duplicated) unstable zeros and poles. To obtain a lower bound of the best achievable H∞ performance for such involved cases, in this paper, we study a dual of the standard LMI that represents the existence of H∞ controllers achieving a prescribed H∞ performance level. By deriving a parametrization of dual feasible solutions and constructing a dual suboptimal solution analytically, we can readily obtain a lower bound of the best achievable H∞ performance..
14. Yoshio Ebihara, Convergence rate analysis of delay interconnected positive systems under formation control, 10th Asian Control Conference, ASCC 2015, 2015.09, This paper is concerned with the analysis of interconnected systems where positive subsystems are connected by a nonnegative interconnection matrix with communication delays. Recently, we have shown that, under mild assumptions on the positive subsystems and the interconnection matrix, the delay interconnected system has stable poles only except for a simple pole at the origin, and the output of the interconnected system converges to a scalar multiple of a prescribed positive vector. This result is effectively used for formation control of multi-agent systems with positive dynamics, where the desired formation is basically achieved irrespective of the length of the delays. However, the rate of convergence varies according to the length of the delays and hence quantitative evaluation of the convergence rate is an important issue. For the quantitative evaluation of the convergence rate, in this paper, we provide an efficient method for the computation of the lower bounds of the second largest real part of the (infinitely many) poles of the delay interconnected positive systems..
15. Yoshio Ebihara, Taiki Matsumura, Tomomichi Hagiwara, Dimitri Peaucelle, Denis Arzelier, Analysis and synthesis of interconnected positive systems with external inputs, 8th IFAC Symposium on Robust Control Design, ROCOND 2015, 2015.07, In this paper, we deal with an interconnected system constructed from positive subsystems and a nonnegative interconnection matrix. In particular, motivated by leader-follower-type formation control of multi-agent systems, we concentrate our attention on the case where external inputs are applied to the interconnected system. By analyzing the steady-state output of the interconnected system with respect to step and ramp inputs, respectively, we derive synthesis conditions on the interconnection matrix to achieve formation-control-oriented design objectives. We finally illustrate the usefulness of theoretical results via numerical simulation on time-head way control of vehicle platoons..
16. Yoshio Ebihara, Analysis and synthesis of delay interconnected positive systems with external inputs and formation control of moving objects, 54th IEEE Conference on Decision and Control, CDC 2015, 2015.02, This paper is concerned with the analysis and synthesis of time-delay interconnected positive systems with external inputs. The interconnected system of interest is constructed from positive subsystems and a nonnegative interconnection matrix, where we assume delays on communications over subsystems. We first analyze the output behavior of the time-delay interconnected positive systems with step and ramp inputs. Then, we second show that the analysis results can be applied to leader-follower-type formation control of moving objects. More precisely, we show a linear-programming-based synthesis condition of the interconnection matrix to achieve a desired formation. We finally demonstrate the effectiveness of the synthesis technique by numerical simulation on time-headway control of a platoon of vehicles..
17. Yoshio Ebihara, Hayato Waki, Noboru Sebe, H∞ performance limitations analysis for SISO systems
A dual LMI approach, 54th IEEE Conference on Decision and Control, CDC 2015, 2015.02, In a very recent study by the first author and his colleagues, a novel LMI-based approach has been proposed to the best achievable H∞ performance limitations analysis for continuous-time SISO systems. Denoting by P and K a plant and a controller, respectively, and assuming that the plant P has an unstable zero, it was shown that a lower bound of the best achievable H∞ performance with respect to the transfer function (1+PK)-1P can be given analytically in terms of the real part of the unstable zero and the first non-zero coefficient of the Taylor expansion of P around the unstable zero. The goal of this paper is to show that, if the plant P has no unstable zeros except for the sole real unstable zero of degree one, then the lower bound shown there is exact. The exactness proof relies on the detailed analysis on the Lagrange dual problem of the SDP characterizing H∞ optimal controllers. More precisely, we show that we can construct an optimal dual solution proving the exactness analytically in terms of the state-space matrices of the plant P and the unstable zero. This analytical expression of the dual optimal solution is also a main result of this study..
18. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Frederic Gouaisbaut, Dominant pole of positive systems with time-delays, 13th European Control Conference, ECC 2014, 2014.07, This paper is concerned with the dominant pole analysis of asymptotically stable time-delay positive systems (TDPSs). It is known that a TDPS is asymptotically stable if and only if its corresponding delay-free system is asymptotically stable, and this property holds irrespective of the length of delays. However, convergence performance (decay rate) should degrade according to the increase of delays and this intuition motivates us to analyze the dominant pole of TDPSs. As a preliminary result, in this paper, we show that the dominant pole of a TDPS is always real. We also construct a bisection search algorithm for the dominant pole computation, which readily follows from recent results on α-exponential stability of asymptotically stable TDPSs. Then, we next characterize a lower bound of the dominant pole as an explicit function of delays. On the basis of the lower bound characterization, we finally show that the dominant pole of an asymptotically stable TDPS is affected by delays if and only if associated coefficient matrices satisfy eigenvalue-sensitivity condition to be defined in this paper. Moreover, we clarify that the dominant pole goes to zero (from negative side) as time-delay goes to infinity if and only if the coefficient matrices are eigenvalue-sensitive..
19. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Efficient convergence rate analysis of multi-agent positive systems under formation control, 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014, 2014.01, This paper addresses the formation control problem of multi-agent systems whose dynamics are all positive. Recently, as a byproduct of the analysis of interconnected positive systems, we have shown an effective way for designing a communication scheme (i.e., an interconnection matrix) over the positive agents so that a prescribed formation can be achieved. For the convergence rate analysis of such multi-agent positive systems under formation control, we propose an efficient algorithm to compute the dominant pole of interconnected positive systems by actively using the positive property of each agent. We illustrate by numerical examples that the proposed algorithm is definitely efficient particularly when the number of agents gets larger..
20. D. Peaucelle, Y. Ebihara, LMI results for robust control design of observer-based controllers, the discrete-time case with polytopic uncertainties, 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014, 2014.01, Design of robust observers is considered in the context of linear discrete-time, time invariant systems. Robustness is achieved with respect to polytopic type uncertainties that affect the dynamics of the plant. At the difference with the uncertainty-free situation, state-feedback/observer separation principle does not hold. Therefore, the observer design has to take into account the state-feedback gain. Results are derived with linear matrix inequality formalism and involve up-to-date slack-variables approach. A numerical example illustrates the results. Limitations of the method are discussed and prospective work for improving these is exposed..
21. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Persistence analysis of interconnected positive systems with communication delays, 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, 2014.01, This is a continuation of our preceding studies on the analysis of interconnected positive systems. Under mild conditions on positive subsystems and a nonnegative interconnection matrix, we showed that the state of the interconnected positive system converges to a positive scalar multiple of a prescribed positive vector. As a byproduct of this property, called persistence, it turned out that the output converges to the positive right eigenvector of the interconnection matrix. This result is effectively used in the formation control of multi-agent positive systems. The goal of this paper is to prove that the essential property of persistence is still preserved under arbitrary (time-invariant) communication delays. In the context of formation control, this preservation indicates that the desired formation is achieved robustly against communication delays, even though the resulting formation is scaled depending upon initial conditions for the state. From a mathematical point of view, the key issue is to prove that the delay interconnected positive system has stable poles only except for a pole of degree one at the origin, even though it has infinitely many poles in general. To this end, we develop frequency-domain (s-domain) analysis for delay interconnected positive systems..
22. D. Peaucelle, Y. Ebihara, Robust stability analysis of discrete-time systems with parametric and switching uncertainties, 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014, 2014.01, Robust stability analysis is investigated for discrete-time linear systems with rational dependency with respect to polytopic type uncertainties. Two type of uncertainties are considered: constant parametric uncertainties and time-varying switching uncertainties. Results are in LMI formalism and proofs involve parameter-dependent, quadratic in the state, Lyapunov functions. The new proposed conditions are shown to extend and merge two important existing results. Conservatism reduction is tackled via a model augmentation technique. Numerical complexity is contained by exploiting the structure of the models with respect to the uncertainties..
23. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Stability and persistence analysis of large scale interconnected positive systems, 2013 12th European Control Conference, ECC 2013, 2013.12, This paper is concerned with the analysis of large-scale interconnected systems constructed from positive subsystems and a nonnegative interconnection matrix. We first show that the interconnected system is admissible and stable if and only if a Metzler matrix built from the coefficient matrices of the positive subsystems and the interconnection matrix is Hurwitz stable. By means of this key lemma, we further provide several results that characterize the admissibility and stability of interconnected systems in terms of the weighted L1-induced norm of each positive subsystem and the Frobenius eigenvalue of the interconnection matrix. Moreover, in the case where every subsystem is SISO, we provide explicit conditions under which the interconnected system has the property of persistence, i.e., the state of the interconnected system converges to a unique strictly positive vector (up to a strictly positive constant multiplicative factor) irrespective of nonnegative and nonzero initial states. We illustrate the effectiveness of the persistence results via formation control of multi-agent systems..
24. Tomohiko Mitani, Shunji Tanaka, Yoshio Ebihara, An efficient algorithm for transmitting power maximization of phased arrays including amplitude degradation, 2013 21st International Symposium on Electromagnetic Theory, EMTS 2013, 2013.09, An efficient algorithm was developed for transmitting power maximization of phased arrays including amplitude degradation. A large-scale phased array will be adopted as transmitting antenna of a solar power satellite project. The amplitude of each antenna element will be degraded at every phase shift due to long-term operation and failure of antenna units. This array problem is formulated as a discrete optimization problem, and decomposed into element-wise subproblems by utilizing the real rotation theorem. Then a polynomial-time algorithm to solve the problem numerically was constructed..
25. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Analysis and synthesis of interconnected SISO positive systems with switching, 52nd IEEE Conference on Decision and Control, CDC 2013, 2013.01, This paper addresses the analysis and synthesis of interconnected systems constructed from SISO positive subsystems and a nonnegative interconnection matrix. We focus on the case where the interconnection matrix switches over a finite set of given nonnegative matrices. By analyzing the existence of a first integral, we clarify a condition under which the state of the interconnected system, starting from any nonnegative initial state, becomes nonnegative and bounded under arbitrary switching. By extending this result, we establish a linearprogramming- based method to synthesize the interconnection matrices to achieve a switching formation control of multi-agent positive systems..
26. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Decentralized control of interconnected positive systems using L 1-induced norm characterization, 51st IEEE Conference on Decision and Control, CDC 2012, 2012.12, This study concerns decentralized control of interconnected positive systems. The main issue is how to design a controller for each subsystem locally so that positivity and stability of the overall interconnected system can be attained. Under a specific interconnection structure, we will show that such a controller can be designed optimally without any information about the rest of the positive subsystems. This achievement is based on our recent characterization of stability of interconnected positive systems in terms of the L1-induced norm of each subsystem, where the L1-induced norm is evaluated with positive weighting vectors that are coupled mutually over the subsystems. The key observation in this study is that, under the specific interconnection structure, we can decouple the L1-induced norm conditions completely. We thus reduce the original stabilization problem into a set of L1-induced norm optimal controller synthesis problems each of which can be solved indeed locally. In particular, the L1-induced norm optimal controller synthesis can be done efficiently by solving a semidefinite programming problem..
27. Yoshio Ebihara, Dual LMI approach to linear positive system analysis, 2012 12th International Conference on Control, Automation and Systems, ICCAS 2012, 2012.12, This paper is concerned with the dual-LMI-based analysis of linear positive systems. As the first contribution, we will show that the cerebrated Perron-Frobenius theorem can be proved concisely via a duality-based argument. On the other hand, in the second part of the paper, we extend the well-known result that a stable Metzler matrix admits a diagonal Lyapunov matrix as the solution of the Lyapunov inequality. More precisely, again via a duality-based argument, we will clarify a necessary and sufficient condition under which a stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries. This new result leads to an alternative proof for the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the L2 gain of positive systems..
28. Jean Francois Tregouet, Denis Arzelier, Dimitri Peaucelle, Yoshio Ebihara, Christelle Pittet, Alexandre Falcoz, Robust H performance of periodic systems with memory
New formulations, analysis and design results, 51st IEEE Conference on Decision and Control, CDC 2012, 2012.12, This paper is devoted to H analysis and synthesis conditions of state-feedback periodic memory controllers, in the framework of periodic uncertain discrete-time systems. The proposed conditions are such that the user is allowed to freely add degrees-of-freedom to the control law which effectively reduces the conservatism of the synthesis condition and decreases the guaranteed H induced norm of the obtained uncertain closed-loop systems. Numerical examples show that for a particular structure of controllers the efficiency of the design theorem can be significantly enhanced by relaxing the structure of slack-variables..
29. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Optimal L1-controller synthesis for positive systems and its robustness properties, 2012 American Control Conference, ACC 2012, 2012.11, In a recent study, we introduced an L1-induced norm (L 1 gain in short) as a performance index for linear time-invariant positive systems, where the L1-norm of the disturbance input and the performance output signals is evaluated with positive weighting vectors. Moreover, we showed that the L1 gain with the weighting vectors plays an essential role in stability analysis of interconnected positive systems. Aiming at extending this result for stabilization of interconnected positive systems, in this paper, we study L1-optimal feedback controller synthesis for positive systems with given weighing vectors. In particular, we will show that an L1-optimal state-feedback gain designed for a fixed positive system and a fixed pair of weighing vectors is robustly optimal against variations on the input matrix, the direct feedthrough matrix of the controlled positive system as well as variations on the weighting vector for the disturbance input signal. This property is of course promising for robust L1-optimal control of uncertain positive systems. We illustrate the robust optimality property by numerical examples..
30. Jean François Trégouët, Yoshio Ebihara, Denis Arzelier, Dimitri Peaucelle, Christelle Pittet, Alexandre Falcoz, Robust stability of periodic systems with memory
New formulations, analysis and design results, 7th IFAC Symposium on Robust Control Design, ROCOND'12, 2012.09, In this paper, the general formulation of periodically time-varying state-feedback controllers with memory is considered for the first time. New analysis and synthesis conditions for robust stability are proposed. The exibility of these new results allows the user to freely add degrees-of-freedom to the control law which appears to effectively reduce the conservatism of the synthesis condition and to increase the stability domain of the closed-loop system in the presence of uncertainties. Furthermore, it is shown that for a particular structure of controllers a more efficient version of the design theorem can be derived by enriching the matrix of slack-variables..
31. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, L 1 gain analysis of linear positive systems and its application, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, 2011.12, In this paper, we focus on L 1 gain analysis problems of linear time-invariant continuous-time positive systems. A positive system is characterized by the strong property that its output is always nonnegative for any nonnegative input. Because of this peculiar property, it is natural to evaluate the magnitude of positive systems by the L 1 gain (i.e. the L 1 induced norm) in terms of the input and output signals. In contrast with the standard L 1 gain, in this paper, we are interested in L 1 gains with weightings on the input and output signals. It turns out that the L 1 gain with weightings plays an essential role in the stability analysis of interconnected positive systems. More precisely, as a main result of this paper, we show that an interconnected positive system is stable if and only if there exists a set of weighting vectors that renders the L 1 gain of each positive subsystem less than unity. As such, using a terminology in the literature, the weighting vectors work as 'separators,' and thus we establish solid separator-based conditions for the stability of interconnected positive systems. We finally illustrate that these separator-based conditions are effective particularly when we deal with robust stability analysis of positive systems against both L 1 gain bounded and parametric uncertainties..
32. Jean François Trégouët, Denis Arzelier, Dimitri Peaucelle, Yoshio Ebihara, Christelle Pittet, Alexandre Falcoz, Periodic FIR controller synthesis for discrete-time uncertain linear systems, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, 2011.12, This paper is concerned with robust state-feedback controller synthesis for discrete-time linear periodic/time-invariant systems subject to polytopic-type parametric uncertainties. In recent studies, some of the authors conceived an LMI-based approach to periodically time-varying memory controller (PTVMC) synthesis and proved that this approach is indeed effective to get less conservative robust controller design procedures. However, since the peculiar controller structure requires to reset memory to zero in a periodic way, it is pointed out that the control performance depends on the timing of implementation. In this paper we tackle this issue and propose a reset-less state-feedback Periodic FIR Controller (PFIRC), which turns out to be suitable to improve robustness on periodic and time-invariant systems. Moreover, as a special case, a design condition is provided for FIR-type LTI controllers that robustly stabilize uncertain LTI systems. Numerical examples illustrate the efficiency of the proposed approaches..
33. Jean François Trégouët, Denis Arzelier, Dimitri Peaucelle, Yoshio Ebihara, Christelle Pittet, Alexandre Falcoz, Periodic H 2 synthesis for spacecraft attitude control with magnetorquers and reaction wheels, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, 2011.12, Particularly attractive for small satellites, the use of magnetic torquers for attitude control is still a difficult problem. Indeed, equations are naturally time-varying and suffers from controllability issues. In this paper, a generic model, taking different kinds of pointing and different kinds of actuators into account, is proposed, linearized and then discretized. Recent studies demonstrate how combining magnetorquers and reaction wheels is attractive. Following this line, latest LMI synthesis techniques for static periodic controller are applied in this paper to the attitude control problem of a spacecraft equipped with both actuation systems. Simulation results are provided, showing the performance of the obtained control law..
34. Tomohiko Mitani, Shunji Tanaka, Yoshio Ebihara, Experimental study on one-dimensional phased array antenna including lossy digital phase shifters for transmitting power maximization, 2011 30th URSI General Assembly and Scientific Symposium, URSIGASS 2011, 2011.11, A large-scale phased array antenna will be adopted as a microwave power transmitter of solar power satellites. The objective of the present study is to maximize transmitting power of a large-scale phased array antenna including lossy digital phase shifters. In the present paper, we describe a newly developed algorithm for transmitting power maximization, and demonstration experiments of a one-dimensional 12-elements phased array antenna including 4-bit lossy digital phase shifters. We confirmed effectiveness of the developed algorithm through the demonstration experiments as well as numerical simulations..
35. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Some conditions for convexifying static H control problems, 2011.01, In this paper, we show that a set of static controllers satisfying a certain level of H performance becomes convex when the underlying generalized plant satisfy several structural conditions. More precisely, we characterize such static H controllers by an LMI with the controller parameters being kept directly as decision variables. The conditions on the generalized plant are not too strict as illustrated by the fact that a sort of mixed sensitivity problems indeed satisfies these conditions. In addition, for the generalized plant of interest, we prove that full-order dynamical H controllers can be characterized by an LMI with simple change of variables. In stark contrast to known LMI formulations, the change of variables does not involve coefficient matrices of the generalized plant. This property is promising when dealing with a whole variety of robust control problems. As an illustration, the real μ synthesis problem is discussed..
36. Yoshio Ebihara, Yusuke Matsuda, Tomomichi Hagiwara, Asymptotic exactness of dual LMI approach for robust performance analysis of uncertain LTI systems, 2010 49th IEEE Conference on Decision and Control, CDC 2010, 2010.12, In the preceding studies we proposed a dual LMI approach for robust performance analysis problems of LTI systems that are affected by parametric uncertainties. By starting from a dual LMI that characterizes a dissipation performance of uncertainty-free LTI systems, we showed that the robust dissipation performance analysis problem can be reduced into a feasibility problem of a polynomial matrix inequality (PMI). Moreover, by applying a linearization to the PMI, we derived an infinite sequence of LMI relaxation problems that allows us to reduce the relaxation gap gradually. Nevertheless, the asymptotic behaviour of this infinite sequence has been open, and this motivates us to study mutual relationship among the dual LMI approach and existing approaches. As the main result of this paper, we prove that our dual LMI approach corresponds to the dual of the polynomial parameter-dependent Lyapunov function approach with matrix sum-of-squares (SOS) relaxations, which is known to be asymptotically exact. Thus we clarify a close relationship between these two approaches that are seemingly very different. This relationship readily leads us to the desired conclusion that the proposed dual LMI approach is asymptotically exact as well..
37. Yoshio Ebihara, Robust H2 control of uncertain discrete-time linear systems with periodically time-varying memory state-feedback, 2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010, 2010.12, This study is concerned with the synthesis of periodically time-varying memory state-feedback controllers (PTVMSFCs) for discrete-time linear systems. In our preceding studies, we have already established a solid theoretical basis for the LMI-based (robust) H-PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H2 performance criterion. In the H2 case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and inequalities for bounding traces that characterize the H2 norm. We can indeed overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H2-PTVMSFC synthesis. Based on this result, we also consider robust H2-PTVMSFC synthesis for polytopictype uncertain LTI systems..
38. Yoshio Ebihara, Noboru Sebe, Decentralized control for discrete-time LTI systems
Lower bound analysis of H performance achievable via LTI controllers, 2010 American Control Conference, ACC 2010, 2010.10, This paper is concerned with the decentralized H controller synthesis problem for discrete-time linear time-invariant (LTI) systems. In spite of intensive research efforts over the last several decades, this problem is believed to be non-convex and still outstanding in general. Therefore most existing approaches resort to heuristic optimization algorithms that do not allow us to draw any definite conclusion on the quality of the designed controllers. To get around this difficult situation, in this paper, we propose convex optimization procedures for computing lower bounds of the H performance that is achievable via decentralized LTI controllers of any order. In particular, we show that sharpened lower bounds can be obtained by making good use of structures of the LTI plant typically observed in the decentralized control setting. We illustrate via numerical examples that these lower bounds are indeed useful to ensure the good quality of decentralized controllers designed by a heuristic optimization..
39. Masayuki Sato, Yoshio Ebihara, Dimitri Peaucelle, Gain-Scheduled state-feedback controllers using inexactly measured scheduling parameters
H2 and H problems, 2010 American Control Conference, ACC 2010, 2010.10, In this note, we address two design problems for Linear Parameter-Varying (LPV) systems; Gain-Scheduled (GS) H2 state-feedback controller design and GS H state-feedback controller design. In sharp contrast to the methods in the literature, the scheduling parameters are supposed to be inexactly measured. The LPV systems are supposed to have polynomially parameter-dependent statespace matrices, and the controllers to be designed are supposed to be rationally parameter-dependent. Using a parametrically affine matrix, which is the inverse of Lyapunov variable, we give formulations for the design of GS H2 and H state-feedback controllers which are robust against the uncertainties in the measured scheduling parameters, in terms of parametrically affine Linear Matrix Inequalities (LMIs). As a special case, our methods include robust controller design using constant Lyapunov variables. Simple numerical examples are included to illustrate our results..
40. Yoshio Ebihara, Yoshinori Fujiwara, Tomomichi Hagiwara, Masayuki Sato, 2DOF control system design for maneuverability matching and gust disturbance rejection in in-flight simulator MuPAL-α, 2010.01, Multipurpose aviation laboratory-α (MuPAL-α) is an experimental aircraft developed by the Japan aerospace exploration agency (JAXA). Its one of the most important functions is to realize in-flight simulation, i.e., to simulate maneuverability of other aircraft via practical flight experiments. To achieve the desired maneuverability matching under model uncertainty and gust disturbance, in this paper, we construct reference feedforward type 2DOF (RFF-2DOF) control system. We will show via numerical simulation that satisfactory results are obtained by constructing RFF-2DOF control system..
41. Yusuke Matsuda, Yoshio Ebihara, Tomomichi Hagiwara, Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, 2009.12, This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these PMI problems are non-convex and hence computationally intractable in general. To get around this difficulty, we construct a sequence of LMI relaxation problems via a simple idea of linearization. In addition, we derive a rank condition on the LMI solution under which the exactness of the analysis result is guaranteed. From the LMI solution satisfying the rank condition, we can easily extract the worst case parameters..
42. Yoshio Ebihara, Yuki Kuboyama, Tomomichi Hagiwara, Dimitri Peaucelle, Denis Arzelier, Further results on periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, 2009.12, In this paper, we enhance the quality of our preceding results on periodically time-varying memory state-feedback controller (PTVMSFC) synthesis for discrete-time linear periodic/time-invariant systems. We firstly revisit PTVMSFC synthesis for certain systems and derive a necessary and sufficient LMI condition for the existence of the desired H-PTVMSFCs. Based on these LMIs, we next consider robust H-PTVMSFC synthesis for polytopic-type uncertain systems and demonstrate that we can obtain less conservative results. We finally derive a test to verify that the designed PTVMSFC is "exact" in the sense that it attains the best achievable robust H performance. This exactness verification test works fine in practice, and we show via numerical examples that exact robust control is indeed possible via PTVMSFCs, even for those problems where the standard static state-feedback fails..
43. Yoshio Ebihara, D. Peaucelle, D. Arzelier, Robustness analysis of uncertain discrete-time linear systems based on system lifting and LMIs, ICROS-SICE International Joint Conference 2009, ICCAS-SICE 2009, 2009.12, In this paper, we propose novel LMI conditions for the stability and l2 gain performance analysis of discretetime linear periodically time-varying (LPTV) systems. These LMIs are convex with respect to all of the coefficient matrices of the LPTV systems and this property is expected to be promising when dealing with several control system analysis and synthesis problems. For example, we can apply those LMIs straightforwadly to robust performance analysis problems of LPTV systems that are affected by polytopic-type uncertainties. Even though our approach for robust performance analysis is conservative in general, we can reduce the conservatism gradually by artificially regarding the original N -periodic system as pN -periodic and increasing p. In addition, thanks to the simple structure of the LMI conditions, we can readily derive a viable test to verify the exactness of the computation results..
44. Yoshio Ebihara, An elementary proof for the exactness of (D,G) scaling, 2009 American Control Conference, ACC 2009, 2009.11, The goal of this paper is to provide an elementary proof for the exactness of the (D,G) scaling applied to the uncertainty structure with one repeated real scalar block and one full complex matrix block. The (D,G) scaling has vast application area around control theory, optimization and signal processing. This is because, by applying the (D,G) scaling, we can convert inequality conditions depending on an uncertain parameter to linear matrix inequalities (LMIs) in an exact fashion. However, its exactness proof is tough, and this stems from the fact that the proof requires an involved matrix formula in addition to the standard Lagrange duality theory. To streamline the proof, in the present paper, we clarify that the involved matrix formula is closely related to a norm preserving dilation under structural constraints. By providing an elementary proof for the norm preserving dilation, it follows that basic results such as Schur complement and congruence transformation in conjunction with the Lagrange duality theory are enough to complete a self-contained exactness proof..
45. Yusuke Onishi, Yoshio Ebihara, Tomomichi Hagiwara, Extracting worst case perturbations for robustness analysis of parameter-dependent LTI systems, 17th World Congress, International Federation of Automatic Control, IFAC, 2008.12, In this paper, we deal with robust performance analysis problems of LTI systems depending on uncertain parameters. By following existing scaling-based approaches, we firstly derive computationally tractable parameter-independent LMI conditions to assess the robust performance, which are conservative in general. What makes the present approach novel is to take the dual of those LMIs so that we can conclude the exactness of the analysis results. More precisely, we clarify that if the computed dual solution satisfies a certain rank condition, then we can ensure that the robust performance is never attained. In particular, we can extract the worst case perturbation that violates the underlying performance. Thus we provide viable tests for the exactness verification of LMI-based robust performance analysis..
46. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, LMI-based periodically time-varying dynamical controller synthesis for discrete-time uncertain linea, 17th World Congress, International Federation of Automatic Control, IFAC, 2008.12, In this paper, we propose a new LMI-based method for robust state-feedback controller synthesis of discrete-time linear periodic/time-invariant systems subject to polytopic uncertainties. In stark contrast with existing approaches that are confined to static controller synthesis, we explore dynamic controller synthesis and reveal a particular periodically time-varying dynamical controller structure that allows LMI-based synthesis. In particular, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based design methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective to achieve less conservative results..
47. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems, 47th IEEE Conference on Decision and Control, CDC 2008, 2008.12, This is a continuation of our preceding study dealing with robust stabilizing controller synthesis for uncertain discrete-time linear periodic/time-invariant systems. In this preceding study, we dealt with the case where the underlying systems are affected by polytopic-type uncertainties and revealed a particular periodically time-varying dynamical controller (PTVDC) structure that allows LMI-based robust stabilizing controller synthesis. Based on these preliminary results, in this paper, we provide LMI conditions for robust H2 and H∞ PTVDC synthesis. One of the salient features of the proposed method is that we can reduce the conservatism and improve the control performance gradually by increasing the period of the controller to be designed. In addition, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based design methods as particular cases. Through numerical experiments, we illustrate that our design method is indeed effective to achieve less conservative results under both the periodic and time-invariant settings. keywords: Robust control, periodic systems, polytopic uncertainties, linear matrix inequalities..
48. Dimitri Peaucelle, Yoshio Ebihara, Denis Arzelier, Robust H2 perfomance of discrete-time periodic systems
LMIs with reduced dimensions, 17th World Congress, International Federation of Automatic Control, IFAC, 2008.12, Recent papers in the field of LMI-based robust control have provided extensions of known results for linear time-invariant systems to the case of periodically time varying linear systems. These results, theoretically satisfactory because formulated in terms of optimization problems of polynomial complexity, may still have limited applications in practice because the number of variables and constraints is very large. The present paper proposes a new formulation of these results that allows to reduce the computational burden both by reducing the number of decision variables and the size of the constraints. Along with this numerical improvement, the paper produces a new modeling of periodic discrete-time systems in descriptor form that is believed promising for future research..
49. Yoshio Ebihara, Tomomichi Hagiwara, Further results on computing the distance to uncontrollability via LMIs, 2007 American Control Conference, ACC, 2007.12, This paper concerns the computation of the distance to uncontrollability (DTUC) of a given controllable pair A ∈ Cn×n and B ∈ Cn×m. This problem can be regarded as a special case of the structured singular value computation problems and motivated from this fact, in our preceding work, we derived an semidefinite program (SDP) to compute the lower bounds of the DTUC. In the first part of this paper, we show via convex duality theory that the lower bounds can be computed by solving a very concise dual SDP. In particular, this dual SDP enables us to derive a rank condition on the dual variable under which the computed lower bound coincides with the exact DTUC. This rank condition is surely effective in practice, and we will show thorough numerical examples that we can obtain exactness certificate even for those problems where the common rank-one exactness principle fails. On the other hand, in the second part of the present paper, we consider the problem to compute the similarity transformation matrix T that maximizes the lower bound of the DTUC of (T-1AT,T-1B). Based on the SDP for the lower bounds computation, we clarify that this problem can be reduced to generalized eigenvalue problem and thus solved efficiently. In view of the correlation between the DTUC and the numerical difficulties of the associated pole placement problem, this computation of the similarity transformation matrix would lead to an effective and efficient conditioning of the pole placement problem for the pair (A, B)..
50. Yoshio Ebihara, Yusuke Onishi, Tomomichi Hagiwara, Robust performance analysis of uncertain LTI systems
Dual LMI approach and verifications for exactness, 46th IEEE Conference on Decision and Control 2007, CDC, 2007.12, This paper addresses robust performance analysis problems of LTI systems affected by real parametric uncertainties. These problems, known also as a special class of structured singular value computation problems, are inherently intractable (NP-hard problems). As such intensive research effort has been made to obtain computationally tractable and less conservative analysis conditions, where linear matrix inequality (LMI) plays an important role. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything directly if the LMI at hand turns out to be infeasible. This motivates us to consider the dual of the LMI and examine the structure of the dual solution, which does exist if the primal LMI is infeasible. By pursuing this direction, in this paper, we provide a rank condition on the dual solution matrix under which we can conclude that the underlying robust performance is never attained. In particular, a set of uncertain parameters that violates the specified performance can readily be obtained. The key idea to derive these results comes from simultaneous diagonalizability property of commuting diagonalizable matrices. The block-moment matrix structure of the dual variable plays an essential role to make good use of this property..
51. Yoshio Ebihara, Tomomichi Hagiwara, Computing the distance to uncontrollability via LMIs
Lower and upper bounds computation and exactness verification, 45th IEEE Conference on Decision and Control 2006, CDC, 2006.12, In this paper, we consider the problem to compute the distance to uncontrollability of a given controllable pair A ∈ Cn×n and B ∈ Cn×m. It is known that this problem is equivalent to computing the minimum of the smallest singular value of [A - zI B] over z ∈ C. With this fact, Gu proposed an algorithm that correctly estimates the distance at a computation cost ο(n6). On the other hand, in the community of control theory, remarkable advances have been made on the techniques to deal with parametrized linear matrix inequalities (LMIs) as well as the analysis of positive polynomials. This motivates us to explore an alternative LMI-based algorithm and shed more insight on the problem to estimate the distance to uncontrollability. In fact, this paper shows that we can establish an effective method to compute a lower bound of the distance by simply applying the existing techniques to solve parametrized LMIs. To obtain an upper bound, on the other hand, we analyze in detail the solutions resulting from the LMI optimization carried out to compute the lower bound. This enables us to estimate the location of the local, but potentially global optimizer z* ∈ C in a reasonable fashion. We thus provide a novel technique to obtain an upper bound of the distance by evaluating the smallest singular value on the estimated optimizer z*. It turns out that the lower and upper bounds are very close in all tested numerical examples. We finally derive an algebraic condition under which the exactness of the suggested computation method of the lower bound can be ensured, based on the convex duality theory. Furthermore, we show that the suggested computation method of the upper bound is closely related to the obtained algebraic condition for the exactness verification..
52. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Tomomichi Hagiwara, Robust H2 performance analysis of uncertain lti systems via polynomially parameter-dependent Lyapunov functions, 5th IFAC Symposium on Robust Control Design, ROCOND'06, 2006.12, In this paper, we address the robust H2 performance analysis problems of linear time-invariant polytopic-type uncertain systems. To obtain numerically verifiable and less conservative analysis conditions, we employ polynomially parameter-dependent Lyapunov functions (PPDLFs) to assess the robust H2 performance and give a sufficient condition for the existence of such PPDLFs in terms of finitely many linear matrix inequalities (LMIs). The resulting LMI conditions turn out to be a natural extension of those known as extended or dilated LMIs in the literature, where the PDLFs employed were restricted to those depending affinely on the uncertain parameters. It is shown that, by increasing the degree of PPDLFs, we can obtain more accurate (no more conservative) analysis results at the expense of increased computational burden. Exactness of the proposed analysis conditions as well as their computational complexity will be examined through numerical experiments..
53. Yoshio Ebihara, Katsutoshi Maeda, Tomomichi Hagiwara, Robust D-stability analysis of uncertain polynomial matrices via polynomial-type multipliers, 2005.01, This paper addresses robust D-stability analysis problems of uncertain polynomial matrices. The underlying idea we follow is that a given polynomial matrix is D-stable if and only if there exist polynomial-type multipliers that render the resulting polynomial matrices to be strictly positive over a specific region on the complex plane. By applying the generalized S-procedure technique, we show that those positivity analysis problems can be reduced into feasibility tests of linear matrix inequalities (LMIs). Thus we can obtain varieties of LMI conditions for (robust) D-stability analysis of polynomial matrices according to the degree/structure of the multipliers to be employed. in particular, we show that existing LMI conditions for robust D-stability analysis can be viewed as particular cases of the proposed conditions, where the degree of the multipliers chosen to be the same as those of the polynomial matrices to be examined. It turns out that, by increasing the degree of the multipliers, we can readily obtain less conservative LMI conditions than the one found in the literature..
54. Yoshio Ebihara, Yoshimichi Ito, Tomomichi Hagiwara, Exact stability analysis of 2-D systems using LMIs, 2004 43rd IEEE Conference on Decision and Control (CDC), 2004.12, In this paper, we propose necessary and sufficient conditions for asymptotic stability analysis of 2-D systems in terms linear matrix inequalities (LMIs). By introducing a guardian map for the set of Schur stable complex matrices, we first reduce the stability analysis problems into nonsingularity analysis problems of parameter-dependent complex matrices. Then, by means of the discrete-time positive real lemma and the generalized S-procedure, we derive LMI-based conditions to verify the asymptotic stability in an exact (i.e., nonconservative) fashion. It turns out that we can reduce the size of LMIs by employing the generalized S-procedure..
55. Yoshio Ebihara, Katsutoshi Maeda, Tomomichi Hagiwara, Generalized S-procedure for inequality conditions on one-vector-lossless sets and linear system analysis, 2004 43rd IEEE Conference on Decision and Control (CDC), 2004.12, The generalized S-procedure, introduced by Iwasaki et al., has proved to be very useful for robustness analysis and synthesis of control systems. This procedure provides a nonconservative way to convert inequality conditions on lossless sets into numerically verifiable conditions represented by linear matrix inequalities (LMIs). In this paper, we introduce a new notion, one-vector-lossless sets, and propose a generalized S-procedure to reduce inequality conditions on one-vector-lossless sets into LMIs without any conservatism. By means of the proposed generalized S-procedure, we can examine various properties of matrix-valued functions over some regions on the complex plane. To illustrate the usefulness, we show that full rank property analysis problems of polynomial matrices over some specific regions on the complex plane can be reduced into LMI feasibility problems. It turns out that many existing results such as Lyapunov's inequalities for stability analysis of linear systems and LMIs for state-feedback controller synthesis can be viewed as particular cases of this result..
56. Yoshio Ebihara, Tomomichi Hagiwara, On model reduction using LMI's, Proceedings of the 2004 American Control Conference (AAC), 2004.11, In this paper, we deal with the problem of approximating a given n-th order LTI system G by an r-th order system Gr where r < n. It is shown that lower bounds of the H∞ norm of the associated error system can be analyzed by using LMI-related techniques. These lower bounds are given in terms of the Hankel singular values of the system G and coincide with those obtained in the previous studies where the analysis of the Hankel operators plays a central role. Thus, this paper provides an alternative proof for those lower bounds via simple algebraic manipulations related to LMI's. Moreover, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the problem is essentially convex and the optimal reduced-order models can be constructed via LMI optimization..
57. Yoshio Ebihara, Tomomichi Hagiwara, Structured Controller Synthesis Using LMI and Alternating Projection Method, 42nd IEEE Conference on Decision and Control, 2003.12, In this paper, we propose new LMI-based conditions to design output-feedback controllers under structural constraints. The conditions are given in terms of LMI's with rank constraints and we solve them by means of the alternating projection algorithm. Even though the algorithm does not ensure global convergence, extensive numerical experiments demonstrate that the proposed design method is promising in designing structured and/or multiobjective controllers, provided that the dimension of the closed-loop systems is not excessively large..
58. Yoshio Ebihara, Tomomichi Hagiwara, A Dilated LMI Approach to Robust Performance Analysis of Linear Time-Invariant Uncertain Systems, 2003 American Control Conference, 2003.11, This paper studies LMI-based robust performance analysis of linear time-invariant systems depending on uncertain parameters. In the case where the coefficient matrices of the system are affine with respect to the uncertain parameters, the standard LMI's are helpful in dealing with such analysis problems provided that we accept the notion of quadratic stability. On the other hand, in the case of rational parameter dependence, the standard LMI's carry some deficiency and thus we need another effort to derive numerically tractable conditions. This paper shows that recently developed dilated LMI's are effective in attacking such robust performance analysis problems. Indeed, applying dilated LMI's leads directly to numerically tractable conditions regardless of the form of the dependence on uncertain parameters. In addition, dilated LMI's enable us to employ parameter-dependent Lyapunov variables to test robust performance, which are known to be quite effective to alleviate the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable..
59. Yoshio Ebihara, Kazuki Tomioka, Tomomichi Hagiwara, A dilated LMI approach to continuous-time gain-scheduled controller synthesis with parameter-dependent Lyapunov variables, 4th IFAC Symposium on Robust Control Design, ROCOND 2003, 2003.01, This paper is concerned with the gain-scheduled controller synthesis for linear parameter varying (LPV) systems. In the case where the state space matrices of the system depend afrinely on the time-varying parameters, the standard linear matrix inequalities (LMI's) are helpful in dealing with such problems provided that we accept the notion of quadratic stability. However, in the case of rational parameter dependence, the standard LMI's carry some deficiency and do not lead to numerically tractable conditions in a straightforward fashion. This paper clarifies that recently developed dilated LMI's are effective in overcoming the difficulties and deriving numerically tractable conditions The dilated LMI's enable us also to employ parameterdependent Lyapunov variables to achieve control objectives, which are known to be promising to alleviate the conservatism stemming from a quadratic (parameter-independent) Lyapunov variable..
60. Yoshio Ebihara, Tomomichi Hagiwara, Robust controller synthesis with parameter-dependent Lyapunov variables
A dilated LMI approach, 41st IEEE Conference on Decision and Control, 2002.12, This paper enhances our previous results on dilated LMI's so that we can address robust controller synthesis problems for continuous-time LTI systems subject to real polytopic uncertainties. The replacement of a constant scalar involved in the previous dilated LMI's by an adjustable parameter is the key to accomplish this extension. The particular form of the extension enables the use of parameter-dependent Lyapunov variables in such a sound way that an advantage of the dilated LMI approach is ensured explicitly in attacking such robust controller synthesis problems. Namely, the dilated LMI approach is shown to achieve better (no worse) results than the conventional one which is restricted to parameter-independent Lyapunov variables, provided that the adjustable parameter is taken to meet a certain simple condition..
61. Yoshio Ebihara, Tomomichi Hagiwara, New dilated LMI characterizations for continuous-time control design and robust multiobjective control, 2002 American Control Conference, 2002.01, It has been recognized recently that the dilation of the LMI characterizations has new potentials in dealing with such involved problems as multiobjective control, robust performance analysis or synthesis for real polytopic uncertainty and so on. Contrary to the success in this direction in the discrete-time setting, analogous characterizations in the continuous-time setting are still open and challenging. The main contribution of this paper is to propose a general procedure to construct such dilated LMI characterizations for continuous-time control design. Because of our particular procedure, the dilated LMI characterizations are proved to have some very nice and interesting features that are to some extent analogous to the ones already obtained in the discrete-time setting..
62. Y. Ebihara, T. Hagiwara, T. Shimomura, Multiobjective state-feedback-control design with non-common LMI solutions
Change of variables via affine functions, 2001 American Control Conference, 2001.01, This paper presents a new approach with non-common linear matrix inequality (LMI) solutions to the multiobjective state-feedback control design problem. A conventional approach is adopting common LMI solutions to avoid a difficulty of non-convex constraints at the sacrifice of conservatism. To get around the conservatism, in this paper, we perform a standard procedure called change of variables and represent the resulting variables as a set of affine functions of new variables. These affine functions are such that they satisfy the non-convex constraints regardless of the new variables. With these affine functions, we readily derive a set of LMI conditions that allow non-common LMI solutions..
63. Yoshio Ebihara, Tomomichi Hagiwara, Mituhiko Araki, Sequential tuning methods of LQ/LQI controllers for multivariable systems and their application to hot strip mills, The 38th IEEE Conference on Decision and Control (CDC), 1999.12, In this study, we propose such sequential tuning methods of multivariable optimal regulators that can be applied to the tuning of control systems under operation. We apply one of these methods to the tuning of LQI servo systems, and carry out the simulation study of the control of a hot strip mill to illustrate the tuning law and show its effectiveness..