1. |
Y. Ebihara, H. Waki, V. Magron, N. H. A. Mai, D. Peaucelle, S. Tarbouriech, l2 induced norm analysis of discrete-time LTI systems for nonnegative input signals and its application to stability analysis of recurrent neural networks, *European Journal of Control*, 2021.10. |

2. |
Bohao Zhu, James Lam, Yoshio Ebihara, Input–output gain analysis of positive periodic systems, *International Journal of Robust and Nonlinear Control*, https://doi.org/10.1002/rnc.5438, 31, 8, 2928-2945, 2021.02, This paper investigates the input-output gains, including ℓ1- and ℓ∞-gains and L1- and L∞-gains, of discrete-time and continuous-time positive periodic systems. For the discrete-time case, the input–output gain can be characterized by linear inequalities. For the continuous-time case, the input–output gain characterization problem turns into the existence problem of a positive periodic vector function. Based on some necessary and sufficient input–output gain conditions, we find the ℓ1- (L1-) gain of discrete-time (continuous-time) positive periodic systems is equivalent to the of ℓ∞- (L∞-) gain of the associated dual systems. Finally, two numerical examples are given to illustrate the results.. |

3. |
H. Waki, Y. Ebihara, N. Sebe, Reduction of SISO H∞ Output Feedback Control Problem, *Linear Algebra and Its Application*, Vol. 610, pp. 321–378, 2021.02. |

4. |
Yoshio Ebihara, Noboru Sebe, Hayato Waki, On Gain-Scheduled State-Feedback Controller Synthesis with Quadratic Stability Condition, *IEEE Control Systems Letters*, 10.1109/LCSYS.2020.2991480, 4, 3, 662-667, Vol. 4, No. 3, pp. 662–667, 2020.07, This letter shows that, as long as continuous-time linear parameter-varying (LPV) systems are concerned, quadratic-stability-based gain-scheduled state-feedback controller synthesis offers no advantage over quadratic-stability-based fixed (parameter-independent) state-feedback controller synthesis in typical control performance specifications. We derive this counterintuitive result by properly extending the previous results on the robust versions of Finsler's lemma and the elimination lemma. We also show that this counterintuitive result is continuous-time LPV system specific, and in the discrete-time LPV system case quadratic-stability-based gain-scheduled state-feedback controller synthesis does bring improvement. These results give a proper warning about the effectiveness of the quadratic-stability-based gain-scheduled state-feedback controller synthesis.. |

5. |
Y. Ebihara, B. Zhu, J. Lam, The Lq/Lp Hankel Norms of Positive Systems, *IEEE Control Systems Letters*, Vol. 4, No. 2, pp. 462–467, 2020.05. |

6. |
Teruki Kato, Yoshio Ebihara, Tomomichi Hagiwara, Analysis of Positive Systems Using Copositive Programming, *IEEE Control Systems Letters*, 10.1109/LCSYS.2019.2946620, 4, 2, 444-449, Vol. 4, No. 2, pp. 444–449, 2020.04, In the field of control, a wide range of analysis and synthesis problems of linear time-invariant (LTI) systems are reduced to semidefinite programming problems (SDPs). On the other hand, in the field of mathematical programming, a class of conic programming problems, so called the copositive programming problem (COP), is actively studied. COP is a convex optimization problem on the copositive cone, and the completely positive cone, the doubly nonnegative cone, and the Minkowski sum of the positive semidefinite cone and the nonnegative cone are also closely related to COP. These four cones naturally appear when we deal with optimization problems described by nonnegative vectors. In this letter, we show that the stability, the H2 and the H∞ performances of LTI positive systems are basically characterized by the feasibility/optimization problems over these four cones. These results can be regarded as the generalization of well-known LMI/SDP-based results on the positive semidefinite cone. We also clarify that in some performances such direct generalization is not possible due to inherent properties of the copositive or the completely positive cone. We thus capture almost entire picture about how far we can generalize the SDP-based results for positive systems to those on the four cones related to COP.. |

7. |
*H*_{∞} Performance Limitation Analysis Using Semidefinite Programming. |

8. |
Yoshio Ebihara, Bohao Zhu, James Lam, The Lq/Lp Hankel Norms of Positive Systems, *IEEE Control Systems Letters*, 10.1109/LCSYS.2019.2952622, 4, 2, 462-467, 2020.02, This letter is concerned with the Lq/Lp Hankel norms of linear time-invariant positive systems, where the Hankel norms are defined as the induced norms from vector-valued Lp -past inputs to vector valued Lq -future outputs. The Lq/Lp Hankel norms are studied in detail for general (nonpositive) LTI systems, and closed-form formulas have been derived for their characterization. However, some of them unavoidably include the absolute integral of impulse responses and/or implicit functions in their characterization and hence there remain difficulties in practical computation. In this letter we show that such difficulties are circumvented for positive systems, where positivity drastically facilitates the characterization of the past input that attains the Hankel norm. We also provide linear-programming- and semidefinite-programming-based characterizations of the Lq/Lp Hankel norms of positive systems, which are useful in the case where we analyze the Lq/Lp Hankel norms of positive systems affected by parametric uncertainties.. |

9. |
Xingwen Liu, Jun Shen, Zhan Shu, Mustapha Ait Rami, Yoshio Ebihara, Guest editorial Theory of positive systems and applications, *IET Control Theory and Applications*, 10.1049/iet-cta.2019.0228, 13, 7, 889-890, 2019.04. |

10. |
Preface to Special Issue on The 5th Multi-symposium on Control Systems. |

11. |
Construction of Externally Positive Systems and Order Reduction for Discrete-Time LTI System Analysis. |

12. |
Yoshio Ebihara, Technical Committee on Systems with Uncertainty [Technical Activities], *IEEE Control Systems*, 10.1109/MCS.2018.2866649, 38, 6, 18 and 144, 2018.12. |

13. |
Yoshio Ebihara, H_{2} Analysis of LTI systems via conversion to externally positive systems, *IEEE Transactions on Automatic Control*, 10.1109/TAC.2017.2767704, 63, 8, 2566-2572, 2018.08, Motivated by recent advances in the study of linear time-invariant (LTI) positive systems, we explore analysis techniques of general, not necessarily positive, LTI 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 LTI system analysis. A typical example is the computation of the H-2 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 LTI system whose impulse response is given by the product of impulse responses of two different LTI systems. Then, as the main result, we reduce the H-2 norm computation problem of a general LTI system into the L-\infty-induced norm computation problem (or L-1 problem in short) of a positive system, by which we can derive various formulas for the H-2 norm computation.. |

14. |
D. Peaucelle, Y. Ebihara, Affine Versus Multi-Affine Models for S-Variable LMI Conditions, *IFAC-PapersOnLine*, 10.1016/j.ifacol.2018.11.179, 51, 25, 453-458, 2018, This paper discusses and compares LMI results built using the S-variable approach starting from equivalent yet different representations of uncertain systems. Using the fact that S-variable results are well suited to handle descriptor systems and that descriptor system modeling is versatile, we compare results in terms of the impact of modeling on the computational burden and on conservatism. Multi-affine representations allow reduced numerical burden while affine representations lead to less conservative results. Numerical examples show that conservatism reduction is not systematic, but is in some cases quite significant without major increase of the numerical burden.. |

15. |
Yoshio Ebihara, Construction of Externally Positive Systems for Discrete-Time LTI System Analysis, *IFAC-PapersOnLine*, 10.1016/j.ifacol.2018.11.178, 51, 25, 447-452, 2018, This paper is concerned with analysis techniques of discrete-time LTI systems via construction of relevant externally positive systems. Recently, the author established a construction method of an externally positive system whose impulse response is given by the square of the original discrete-time LTI SISO system to be analyzed. This externally positive system allows us to characterize the H_{2} norm of the original system by means of the l_{∞}-induced norm characterization of externally positive systems. It is nonetheless true that, for the original system of order n, the order of the resulting externally positive system is n^{2} and hence this leads to the increase of associated computational burden. With this important issue in mind, in this paper, we show that the order can be reduced down to n(n + 1)/2 by using the elimination and duplication matrices that are intensively studied by Jan R. Magnus in the 80's. In addition to the computational complexity reduction for the aforementioned H_{2} analysis, we show that such construction of externally positive systems with reduced order is quite effective in semidefinite-programming-based peak value analysis of impulse responses of general LTI systems.. |

16. |
Hiroyuki Ichihara, Shoya Tanabe, Yoshio Ebihara, Dimitri Peaucelle, Analysis and Synthesis of Discrete-Time Interconnected Positive Systems, *SICE Journal of Control, Measurement, and System Integration*, 10.9746/jcmsi.11.91, 11, 2, 91-99, 2018.01, This paper presents analysis and synthesis of interconnected systems where the interconnected system of interest consists of discrete-time positive subsystems and an interconnection matrix. The paper gives sufficient conditions for the discrete-time single-input single-output (SISO) subsystems and the interconnection matrix so that the interconnected system has the property of persistence. The fundamental differences for the persistence between the conditions of the discrete-time setting and those of a continuous-time setting are also discussed. The obtained analysis result can apply to formation control for multi-agent systems, which is a synthesis part of the paper. Numerical examples including formation control of mobile robots are shown to illustrate the proposed formation control design method.. |

17. |
*H*_{2 }Analysis of LTI Discrete-Time Systems via Conversion to Externally Positive Systems. |

18. |
Nonlinear Output Feedback Control for Average Output Voltage of Boost Converters Based on their Discretized Bilinear Model. |

19. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Steady-state analysis of delay interconnected positive systems and its application to formation control, *IET Control Theory and Applications*, 10.1049/iet-cta.2017.0315, 11, 16, 2783-2792, 2017.11, This study is concerned with the analysis and synthesis of delay interconnected positive systems. For delay-free cases, it has been shown very recently that the output of the interconnected positive system converges to a positive scalar multiple of a prescribed positive vector under mild conditions on positive subsystems and a non-negative interconnection matrix. This result is effectively used for formation control of multi-agent systems with positive dynamics. The goal of this study is to prove that this steady-state property is essentially preserved under any constant (and hence bounded) communication delay. 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 on initial conditions for the state. To ensure the achievement of the steady-state property, the authors need to prove rigorously 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. For the rigorous proof, we newly develop frequency-domain (s-domain) analysis for delay interconnected positive systems, which has not been studied for delay-free cases.. |

20. |
Hiroyuki Ichihara, Shinya Kajihara, Yoshio Ebihara, Dimitri Peaucelle, Formation Control of Mobile Robots Based on Interconnected Positive Systems, *IFAC-PapersOnLine*, 10.1016/j.ifacol.2017.08.755, 50, 1, 8441-8446, 2017.07, This paper deals with formation control of mobile robots based on interconnected positive systems with SISO subsystems where each robot has a nonlinear dynamics of a MIMO subsystem. To linearize the dynamics, this paper introduces a virtual vehicle of the robot. Then a feedback linearization and a local feedback law transform each dynamics of the virtual vehicle into two SISO positive and stable linear systems. Consequently, the dynamics of the virtual vehicles satisfy the properties of the interconnected positive systems. Experimental results as well as numerical examples including leader-follower formation control for the mobile robots are illustrated.. |

21. |
Shoya Tanabe, Hiroyuki Ichihara, Yoshio Ebihara, Dimitri Peaucelle, Persistence Analysis of Discrete-Time Interconnected Positive Systems and its Application to Mobile Robot Formation, *IFAC-PapersOnLine*, 10.1016/j.ifacol.2017.08.304, 50, 1, 3105-3110, 2017.07, This paper addresses the analysis of discrete-time interconnected systems where each subsystem is stable and positive. Admissibility and persistence notions are derived similar to the continuous-time case and a condition for enforcing persistence is derived for the case when all subsystems are single-input single output. Results are applied on numerical examples including the formation control of mobile robots.. |

22. |
Yoshio Ebihara, Stability Analysis of Neutral Type Time-Delay Positive Systems with Commensurate Delays, *IFAC-PapersOnLine*, 10.1016/j.ifacol.2017.08.681, 50, 1, 3093-3098, 2017.07, Recently, the author derived a necessary and sufficient condition for the asymptotic stability of neutral type time-delay positive systems (TDPSs), where the neutral type TDPS of interest is given by a feedback connection between a finite-dimensional LTI positive system and the pure delay The goal of this paper is to extend this result to neutral type TDPSs with multiple commensurate delays. To this end, we first represent a neutral type TDPS with multiple commensurate delays as a neutral type TDPS with a single delay, by augmenting input and output signals in the feedback connection. By this conversion, we can readily apply the latest result already established for single delay neutral type TDPSs. As the main result, we show that a neutral type TDPS with commensurate delays is stable if and only if its delay-free counterpart is stable and an additional “admissibility” condition is satisfied. This result in particular implies that the stability is irrelevant of the length of delays.. |

23. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Analysis and synthesis of interconnected positive systems, *IEEE Transactions on Automatic Control*, 10.1109/TAC.2016.2558287, 62, 2, 652-667, 2017.02, This paper is concerned with the analysis and synthesis of interconnected systems constructed from heterogeneous positive subsystems and a nonnegative interconnection matrix. We first show that admissibility, to be defined in this paper, is an essential requirement in constructing such interconnected systems. Then, we clarify that the interconnected system is admissible and stable if and only if a Metzler matrix, which is built from the coefficient matrices of positive subsystems and the nonnegative interconnection matrix, is Hurwitz stable. By means of this key result, we further provide several results that characterize the admissibility and stability of the interconnected system in terms of the Frobenius eigenvalue of the interconnection matrix and the weighted L_{1}- induced norm of the positive subsystems again to be defined in this paper. 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., its state converges to a unique strictly positive vector (that is known in advance up to a strictly positive constant multiplicative factor) for any nonnegative and nonzero initial state. As an important consequence of this property, we show that the output of the interconnected system converges to a scalar multiple of the right eigenvector of a nonnegative matrix associated with its Frobenius eigenvalue, where the nonnegative matrix is nothing but the interconnection matrix scaled by the steady-stage gains of the positive subsystems. This result is then naturally and effectively applied to formation control of multiagent systems with positive dynamics. This result can be seen as a generalization of a well-known consensus algorithm that has been basically applied to interconnected systems constructed from integrators.. |

24. |
Dimitri Peaucelle, Yoshio Ebihara, Yohei Hosoe, Robust observed-state feedback design for discrete-time systems rational in the uncertainties, *Automatica*, 10.1016/j.automatica.2016.10.003, 76, 96-102, 2017.02, Design of controllers in the form of a state-feedback coupled to a state observer is studied in the context of uncertain systems. The classical approach by Luenberger is revisited. Results provide a heuristic design procedure that mimics the independent state-feedback/observer gains design by minimizing the coupling of observation error dynamics on the ideal state-feedback dynamics. The proposed design and analysis conditions apply to linear systems rationally-dependent on uncertainties defined in the cross-product of polytopes. Convex linear matrix inequality results are given thanks to the combination of a descriptor multi-affine representations of systems and the S-variable approach. Stability and H_{∞} performances are assessed by multi-affine parameter-dependent Lyapunov matrices.. |

25. |
Analysis and Synthesis of Positive Systems and Copositive Programming. |

26. |
Yoshio Ebihara, Technical Committee on Systems with Uncertainty [Technical Activities], *IEEE Control Systems*, 10.1109/MCS.2016.2584278, 36, 5, 2016.10. |

27. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Convergence Rate Analysis of Multi-Agent Positive Systems under Formation Control An Efficient Algorithm by Exploiting Positivity, *SICE Journal of Control, Measurement, and System Integration*, 10.9746/jcmsi.9.216, 9, 5, 216-224, 2016.09, This paper is concerned with convergence rate analysis of multi-agent positive systems under formation control. Recently, we have shown that very basic multi-agent systems under formation control can be modeled as interconnected positive systems, and desired formation can be achieved by designing interconnection matrices appropriately. In such formation control, the resulting convergence performance (i.e., convergence rate) varies according to the interconnection matrices and this fact motivates us to develop an efficient algorithm for the analysis of the convergence rate. In this paper, assuming that the dynamics of agents are positive and homogeneous, we conceive such an algorithm by problem decomposition. We show that the decomposition to smaller size problems and drastic reduction of computational burden become possible by making full use of the positivity of the agents.. |

28. |
Yoshio Ebihara, Keisuke Matsuo, Tomomichi Hagiwara, LMI-Based Lower Bound Analysis of the Best Achievable *H*_{∞} Performance for SISO Systems, *SICE Journal of Control, Measurement, and System Integration*, 10.9746/jcmsi.9.165, 9, 4, 165-172, 2016.07, In this paper, we study *H*_{∞} performance limitation analysis for continuous-time SISO systems using LMIs. By starting from an LMI that characterizes a necessary and sufficient condition for the existence of desired controllers achieving a prescribed *H*_{∞} performance level, we represent lower bounds of the best *H*_{∞} performance achievable by any LTI controller in terms of the unstable zeros and the unstable poles of a given plant. The transfer functions to be investigated include the sensitivity function (1+*PK*)^{-1}, the complementary sensitivity function (1+*PK*)^{-1}*PK*, and (1+*PK*)^{-1}*P*, the first and the second of which are well investigated in the literature. As a main result, we derive lower bounds of the best achievable *H*_{∞} performance with respect to (1+*PK*)^{-1}*P* assuming that the plant has unstable zeros. More precisely, we characterize a lower bound in closed-form by means of the first non-zero coefficient of the Taylor expansion of the plant *P*(*s*) around its unstable zero.. |

29. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Descriptor case and system augmentation, *Communications and Control Engineering*, 10.1007/978-1-4471-6606-1_3, 61-106, 2015.01, Chapter 3 is an extension of the SV-LMIs of the preceding chapter both in terms of generalization of the results and for further conservatism reduction. First the SV results are generalized to descriptor systems. Not only this result is valuable in itself, but, combined to a model manipulation technique, an infinite sequence of SV-LMIs can be build. This sequence of SV-LMIs is shown to be easy to construct and proved to be of decreasing conservatism. Tests are provided for checking if the conservatism gap vanishes. On examples it is shown that the conservatism gap indeed vanishes and this is obtained early elements of the sequence (i.e., the convergence is rather fast).. |

30. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Introduction, *Communications and Control Engineering*, 10.1007/978-1-4471-6606-1_1, 9781447166054, 1-8, 2015.01, Chapter 1 is dedicated to the origins of the “ S -variable approach.” We trace the contributions of independent authors that participated to establish the fundamentals and justify our choice for the denomination “ S -variable approach.” This attentive detailed study is the occasion to show several interpretations of the S -variables with respect to technical results such as Finsler’s lemma and elimination lemma. The chapter concludes with the brief exposure of all the problems to be tackled in the remaining part of the book, justifying the importance of these selected problems.. |

31. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Multiobjective controller synthesis for LTI systems, *Communications and Control Engineering*, 10.1007/978-1-4471-6606-1_5, 139-164, 2015.01, Chapter 5 focuses on multiobjective control design problems for discrete-time LTI systems. The goal here is to design a controller that satisfy multiple (and typically conflicting) design specifications. In the state-feedback case, the advantage of the SV-LMIs readily follows from the synthesis results in Chap. 4. To handle output-feedback case, we first extend the results of Chap. 4 and provide SV-LMI-based formulas for dynamic output-feedback controller synthesis. Then, the effectiveness of the SV-LMIs in conservatism reduction can be shown almost the same way as in the state-feedback case.. |

32. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Robust controller synthesis of periodic discrete-time systems, *Communications and Control Engineering*, 10.1007/978-1-4471-6606-1_8, 229-244, 2015.01, Finally, Chapter 8 deals with state-feedback controller synthesis for discrete-time periodic systems. By introducing S-variables and applying change of variables that is almost identical to the LTI case, we can readily obtain SV-LMIs for periodic state-feedback controller synthesis. We illustrate by numerical examples that the SV-LMIs are indeed effective in conservatism reduction when dealing with discrete-time periodic systems affected by polytopic uncertainties.. |

33. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Robust performance analysis of LTI systems, *Communications and Control Engineering*, 10.1007/978-1-4471-6606-1_2, 9-59, 2015.01, The primary goal of Chap. 2 is founding the basic idea of the SV approach. Before generalizing the technique (which is done in the following chapters), we show its effectiveness on simple essential control problems. We mainly consider the robust performance analysis problems of linear time-invariant systems affected by parametric uncertainties, and clarify why the SV-LMIs do perform well on these intractable infinite-dimensional semi-infinite problems. We also highlight the improvements in terms of conservatism both theoretically and on examples.. |

34. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Robust performance analysis of discrete-time periodic systems, *Communications and Control Engineering*, 10.1007/978-1-4471-6606-1_7, 199-227, 2015.01, Chapter 7 is dedicated to the analysis of discrete-time periodic systems by means of SV-LMIs. For that special case the SV-LMIs have interesting non-causal system interpretations. Similarly to the LTI case, SV-LMIs are effective for reducing the conservatism of the analysis results when dealing with discrete-time periodic systems affected by polytopic uncertainties.. |

35. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Robust state-feedback synthesis for LTI systems, *Communications and Control Engineering*, 10.1007/978-1-4471-6606-1_4, 107-137, 2015.01, In this chapter, the SV-LMIs of Chap. 2 are reconsidered for robust state-feedback synthesis. The results rely on the structuring of the S-variables. An interpretation in terms of virtual stable model is given to this structure. Moreover, we show the effect of this structuring on conservatism reduction. It happens to be of different nature in the discrete-time and continuous-time cases.. |

36. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Static output-feedback synthesis, *Communications and Control Engineering*, 10.1007/978-1-4471-6606-1_6, 165-198, 2015.01, While the two previous chapters address control design cases which have LMI solutions, Chap. 6 tackles the hard problem of static output-feedback design. No polynomial-time optimization method exists for that problem, and if keeping in the matrix inequality framework, one has to resort to iterative LMI algorithms. For that important and hard problem, the SV approach produces a sophisticated version of such iterative LMI algorithm. In this case, the structuring of the S-variables reveals a virtual stabilizing state feedback. This original design procedure is detailed and tested on examples.. |

37. |
Analysis and Synthesis of Interconnected Positive Systems(Control and Mathematics of Positive Systems). |

38. |
Dominant Pole Analysis of Linear Positive Systems with Multiple Time-Delays. |

39. |
Nonlinear Control with Integral Compensation for Output Voltage of Boost Converters Based on Discretized Bilinear Model―I:―Modeling and Identification. |

40. |
Nonlinear Control with Integral Compensation for Output Voltage of Boost Converters Based on Discretized Bilinear Model―II:―Derivation of a Control Law and Verification by Experiments. |

41. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Frédéric Gouaisbaut, Dominant pole analysis of stable time-delay positive systems, *IET Control Theory and Applications*, 10.1049/iet-cta.2014.0375, 8, 17, 1963-1971, 2014.11, This study 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 analyse the dominant pole of TDPSs. As a preliminary result, in this study, the authors show that the dominant pole of a TDPS is always real. They also construct a bisection search algorithm for the dominant pole computation, which readily follows from recent results on á-exponential stability of asymptotically stable TDPSs. Then, they next characterise a lower bound of the dominant pole as an explicit function of delays. On the basis of the lower bound characterisation, they 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 study. Moreover, they 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.. |

42. |
Yoshio Ebihara, Noboru Sebe, Lower bound analysis of H∞ performance achievable via decentralized LTI controllers, *International Journal of Robust and Nonlinear Control*, 10.1002/rnc.2999, 24, 16, 2423-2437, 2014.11, This paper is concerned with the decentralized H∞ controller synthesis problem for discrete-time LTI systems. Despite of intensive research efforts over the last several decades, this problem is believed to be nonconvex and still outstanding in general. Therefore, most of 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 difficulty, 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 will 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.. |

43. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, On the structure of generalized plant convexifying static H∞ control problems, *Automatica*, 10.1016/j.automatica.2014.04.027, 50, 6, 1706-1714, 2014.06, This paper shows that, under specific structures of generalized plants, the set of static controllers satisfying internal stability and a certain level of H∞ performance becomes convex. More precisely, we characterize such static H∞ controllers by an LMI with controller variables being kept directly as decision variables. The structural conditions on the generalized plant are not too strict, and we show that generalized plants corresponding to a sort of mixed sensitivity problems indeed satisfy these conditions. For the generalized plants of interest, we further prove that full-order dynamical H∞ controllers can be characterized by an LMI with a simple change of variables. In stark contrast to the known LMI-based H∞ controller synthesis, the change of variables is free from the coefficient matrices of the generalized plant and this property is promising when dealing with a variety of robust control problems. Related issues such as robust controller synthesis against real parametric uncertainties are also discussed.. |

44. |
Shunji Tanaka, Tomohiko Mitani, Yoshio Ebihara, An efficient beamforming algorithm for large-scale phased arrays with lossy digital phase shifters, *IEICE Transactions on Communications*, 10.1587/transcom.E97.B.783, E97-B, 4, 783-790, 2014.01, An efficient beamforming algorithm for large-scale phased arrays with lossy digital phase shifters is presented. This problem, which arises in microwave power transmission from solar power satellites, is to maximize the array gain in a desired direction with the gain loss of the phase shifters taken into account. In this paper the problem is first formulated as a discrete optimization problem, which is then decomposed into element-wise subproblems by the real rotation theorem. Based on this approach, a polynomial-time algorithm to solve the problem numerically is constructed and its effectiveness is verified by numerical simulations.. |

45. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, LMI approach to linear positive system analysis and synthesis, *Systems and Control Letters*, 10.1016/j.sysconle.2013.11.001, 63, 1, 50-56, 2014.01, This paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities (LMIs). We first show that the celebrated Perron-Frobenius theorem can be proved concisely by a duality-based argument. Again by duality, we next clarify a necessary and sufficient condition under which a Hurwitz stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries as the solution of the Lyapunov inequality. This new result leads to an alternative proof of the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the H_{∞} performance of continuous-time positive systems. In addition, we further derive a new LMI for the H_{∞} performance analysis where the variable corresponding to the Lyapunov matrix is allowed to be non-symmetric. We readily extend these results to discrete-time positive systems and derive new LMIs for the H_{∞} performance analysis and synthesis. We finally illustrate their effectiveness by numerical examples on robust state-feedback H_{∞} controller synthesis for discrete-time positive systems affected by parametric uncertainties.. |

46. |
Simultaneous Optimization of Phases and Amplitudes for Wireless Power Transmission by a Large-Scale Phased Array Antenna with Lossy Digital Phase Shifters. |

47. |
**Maximum Power Point Tracking Control of Photovoltaic ****Systems Based on Particle Swarm Optimization with Experimental Verication**. |

48. |
Jean François Trégouët, Dimitri Peaucelle, Denis Arzelier, Yoshio Ebihara, Periodic memory state-feedback controller New formulation, analysis, and design results, *IEEE Transactions on Automatic Control*, 10.1109/TAC.2013.2251820, 58, 8, 1986-2000, 2013.08, This paper proposes a unified setup for robust stability and performance analysis and synthesis for periodic polytopic discrete-time systems. Relying on a general formulation for state-feedback periodic memory controllers and a new time-lifting, new sufficient LMI conditions for the existence of robust stability certificates and H_{2} guaranteed cost control laws are derived. Comparisons of the efficiency of different controller structures illustrate these developments on a numerical example.. |

49. |
Yoshio Ebihara, Periodically time-varying memory state-feedback for Robust H_{2} control of uncertain discrete-time linear systems, *Asian Journal of Control*, 10.1002/asjc.541, 15, 2, 409-419, 2013.03, 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 linear matrix inequality (LMI)-based (robust) H _{∞}-PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H _{2} performance criterion. In the H _{2} 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 the inequalities for bounding traces that characterize the H _{2} norm. We can overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H _{2}-PTVMSFC synthesis. On the basis of this result, we also consider robust H _{2}-PTVMSFC synthesis for LTI systems with parametric uncertainties.. |

50. |
LMI-based Stability and H_∞ Performance Analysis of Discrete-time Positive Systems. |

51. |
The 50th IEEE Conference on Decision and Control and European Control Conference(International Conference). |

52. |
Yoshio Ebihara, Jun Yamaguchi, Tomomichi Hagiwara, Periodically time-varying controller synthesis for multiobjective H _{2} H_{∞} control of discrete-time systems and analysis of achievable performance, *Systems and Control Letters*, 10.1016/j.sysconle.2011.05.008, 60, 9, 709-717, 2011.09, In this paper, we propose a linear periodically time-varying (LPTV) controller synthesis approach for the multiobjective H_{2}H _{∞} control problem of discrete-time linear time-invariant (LTI) systems. By artificially regarding the LTI plant as N-periodic and applying the discrete-time system lifting, we first derive a sequence of semidefinite programmings (SDPs) indexed by N for the synthesis of suboptimal multiobjective LPTV controllers. Furthermore, we show that we can reduce the conservatism and improve the control performance gradually by simply increasing the controller period N. On the other hand, in the latter part of the paper, we propose another sequence of SDPs for the computation of the lower bound of the multiobjective control performance that is achievable via LPTV controllers of any period and order. Similarly to the LPTV controller synthesis, the SDP is derived based on the lifting-based treatment of the LTI plant. Again, it is shown that we can improve the lower bound gradually by increasing the fictitious period N. We validate all of these theoretical results through illustrative examples.. |

53. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems, *Automatica*, 10.1016/j.automatica.2010.10.004, 47, 1, 14-25, 2011.01, In this paper, we deal with discrete-time linear periodic/time-invariant systems with polytopic-type uncertainties and propose a new linear matrix inequality (LMI)-based method for robust state-feedback controller synthesis. In stark contrast with existing approaches that are confined to memoryless static controller synthesis, we explore dynamical controller synthesis and reveal a particular periodically time-varying memory state-feedback controller (PTVMSFC) structure that allows LMI-based synthesis. In the context of robust controller synthesis, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based static controller synthesis methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective in achieving less conservative results, under both periodic and time-invariant settings. We finally derive a viable test to verify that the designed robust PTVMSFC is "exact" in the sense that it attains the best achievable robust performance. This exactness verification test works fine in practice, and we will show via a numerical example that exact robust control is indeed attained by designing PTVMSFCs, even for such a problem where the standard memoryless static state-feedback fails.. |

54. |
Control System Analysis and Synthesis Based on Linear Matrix Inequalities(Applications of Numerical/Symbolic Computation Software to Control System Analysis and Synthesis). |

55. |
Robust H_∞ Performance Analysis of LTI Systems with a Single Uncertain Parameter. |

56. |
Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Analysis of uncertain discrete-time linear periodic systems based on system lifting and LMIs, *European Journal of Control*, 10.3166/ejc.16.532-544, 16, 5, 532-544, 2010.01, In this article, we propose novel linear matrix inequality (LMI) conditions for the stability and l_{2} gain performance analysis of discrete-time 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 promising when we deal with several control system analysis and synthesis problems. For example, we can apply those LMIs straightforwardly 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.. |

57. |
Periodically time-varying memory state feedback controller synthesis for discrete-time LTI systems with parametric uncertainties described by LFT. |

58. |
Maximization of Wireless Transmitting Power by Phase Optimization of Array Antennas on a Solar Power Satellite. |

59. |
Attitude Control of an Experimental Helicopter by a 2DOF Controller with Inverse-System Based Design of the Feedforward. |

60. |
Verifying the Effectiveness of the Lower Bounds of the Optimal Performances in the Decentralized H-infinity Control Problems of Discrete-Time LTI Systems. |

61. |
Simple Adaptive Control Synthesis Enhanced by Scaling and Its Application to Positioning Control of Antagonist-Type Pneumatic Actuation Mechanism. |

62. |
Yoshio Ebihara, Yusuke Onishi, Tomomichi Hagiwara, Robust performance analysis of uncertain LTI systems Dual LMI approach and verifications for exactness, *IEEE Transactions on Automatic Control*, 10.1109/TAC.2009.2017086, 54, 5, 938-951, 2009.05, This paper addresses robust performance analysis problems of linear time-invariant (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. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything 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. By pursuing this direction, in this paper, we provide rank conditions 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 be computed. These results come from block-moment matrix structure of the dual variable, which is consistent with the recent results on polynomial optimization. This particular structure enables us to make good use of simultaneous diagonalizability property of commuting diagonalizable matrices so that the sound rank conditions for the exactness verification can be obtained.. |

63. |
Yoshio Ebihara, Yusuke Onishi, Tomomichi Hagiwara, Robust Performance Analysis of Uncertain LTI Systems Dual LMI Approach and Verifications for Exactness, *IEEE Transactions on Automatic Control*, 54, 5, 938-951, 2009.05, This paper addresses robust performance analysis problems of linear time-invariant (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. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything 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. By pursuing this direction, in this paper, we provide rank conditions 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 be computed. These results come from block-moment matrix structure of the dual variable, which is consistent with the recent results on polynomial optimization. This particular structure enables us to make good use of simultaneous diagonalizability property of commuting diagonalizable matrices so that the sound rank conditions for the exactness verification can be obtained.. |

64. |
Periodically Time-Varying Memory State-Feedback Controller Synthesis for Uncertain Discrete-Time Linear Systems:The H2 Case. |

65. |
Yoshio Ebihara, Katsutoshi Maeda, Tomomichi Hagiwara, Generalized S-procedure for inequality conditions on one-vector-lossless sets and linear system analysis, *SIAM Journal on Control and Optimization*, 10.1137/050627551, 47, 3, 1547-1555, 2008.11, The generalized version of the S-procedure, recently introduced by Iwasaki and co-authors and Scherer independently, has proved to be very useful for robustness analysis and synthesis of control systems. In particular, this procedure provides a nonconservative way to convert specific 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 and LMIs for state-feedback controller synthesis readily follow from the suggested generalized S-procedure.. |

66. |
Yoshio Ebihara, On the Exactness Proof of (D, G) Scaling, *SICE Journal of Control, Measurement, and System Integration*, 10.9746/jcmsi.1.474, 1, 6, 474-478, 2008.11, The goal of this paper is to provide an elementary proof for the exactness of the (*D*,*G*) scaling. 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.. |

67. |
Trajectory Tracking Control of a Two-axis Arm Driven by Pneumatic Artificial Muscles. |

68. |
Yoshio Ebihara, Computing the distance to uncontrollability via LMIs Lower bound computation with exactness verification, *Systems and Control Letters*, 10.1016/j.sysconle.2008.03.002, 57, 9, 763-771, 2008.09, In this paper, we consider the problem of computing the distance to uncontrollability (DTUC) of a given controllable pair A ∈ C^{n × n} and B ∈ C^{n × m}. It is known that this problem is equivalent to computing the minimum of the smallest singular value of [A - z I B] over z ∈ C. With this fact, Gu et al. proposed an algorithm that correctly estimates the DTUC at a computation cost O (n^{4}). From the viewpoints of linear control system theory, on the other hand, this problem can be regarded as a special case of the structured singular value computation problems and thus it is expected that we can establish an alternative LMI-based algorithm. In fact, this paper first shows that we can compute a lower bound of the DTUC by simply applying the existing techniques to solve robust LMIs. Moreover, we show via convex duality theory that this lower bound can be characterized by a very concise dual SDP. In particular, this dual SDP enables us to derive a condition on the dual variable under which the computed lower bound surely coincides with the exact DTUC. On the other hand, in the second part of the paper, we consider the problem of computing the similarity transformation matrix T that maximizes the lower bound of the DTUC of (T^{- 1} A T, T^{- 1} B). We clarify that this problem can be reduced to a 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 transformation matrix would lead to an effective and efficient conditioning of the pole placement problem for the pair (A, B).. |

69. |
Yoshio Ebihara, Yoshito Hirai, Tomomichi Hagiwara, On H∞ model reduction for discrete-time linear time-invariant systems using linear matrix inequalities, *Asian Journal of Control*, 10, 3, 291-300, 2008.05, In this paper, we address the H∞ model reduction problem for linear time-invariant discrete-time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well-known lower bounds on the approximation error, which is given in terms of the Hankel singular values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the H∞ optimal reduced-order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting.. |

70. |
Yoshio Ebihara, Katsutoshi Maeda, Tomomichi Hagiwara, Generalized $mathcal{S}$-Procedure for Inequality Conditions on One-Vector-Lossless Sets and Linear System Analysis, *SIAM Journal on Control and Optimization*, 47, 3, 1547-1555, 2008, The generalized version of the $mathcal{S}$-procedure, recently introduced by Iwasaki and co-authors and Scherer independently, has proved to be very useful for robustness analysis and synthesis of control systems. In particular, this procedure provides a nonconservative way to convert specific 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 $mathcal{S}$-procedure to reduce inequality conditions on one-vector-lossless sets into LMIs without any conservatism. By means of the proposed generalized $mathcal{S}$-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 and LMIs for state-feedback controller synthesis readily follow from the suggested generalized $mathcal{S}$-procedure.. |

71. |
Atitude Control of a Experimental Helicopter with a 2DOF-LQI Design Method. |

72. |
Robust H2 Performance Analysis of Continuous-Time LTI Systems Affected by Parametric Uncertainties. |

73. |
Robust Performance Analysis of Uncertain LTI Systems based on Dual LMIs. |

74. |
Modeling of Cuk Converters based on Discretization ofState Equations and Its Experimental Verification. |

75. |
Positioning Control of a Pneumatic Actuation Mechanism of Antagonist-Type Based on Simple Adaptive Control. |

76. |
Yoshio Ebihara, Yoshimichi Ito, Tomomichi Hagiwara, Exact stability analysis of 2-D systems using LMIs, *IEEE Transactions on Automatic Control*, 10.1109/TAC.2006.880789, 51, 9, 1509-1513, 2006.09, In this note, we propose necessary and sufficient conditions for the asymptotic stability analysis of two-dimensional (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 that enable us to analyze the asymptotic stability in an exact (i.e., nonconservative) fashion. It turns out that, by employing the generalized S-procedure, we can derive smaller size of LMIs so that the computational burden can be reduced.. |

77. |
Yoshio Ebihara, Tomomichi Hagiwara, On the degree of polynomial parameter-dependent Lyapunov functions for robust stability of single parameter-dependent LTI systems A counter-example to Barmish's conjecture, *Automatica*, 10.1016/j.automatica.2006.04.011, 42, 9, 1599-1603, 2006.09, In this paper, we consider the robust Hurwitz stability analysis problems of a single parameter-dependent matrix A (θ) {colon equals} A_{0} + θ A_{1} over θ ∈ [- 1, 1], where A_{0}, A_{1} ∈ R^{n × n} with A_{0} being Hurwitz stable. In particular, we are interested in the degree N of the polynomial parameter-dependent Lyapunov matrix (PPDLM) of the form P (θ) {colon equals} ∑_{i = 0}^{N} θ^{i} P_{i} that ensures the robust Hurwitz stability of A (θ) via P (θ) > 0, P (θ) A (θ) + A^{T} (θ) P (θ) < 0 (∀ θ ∈ [- 1, 1]). On the degree of PPDLMs, Barmish conjectured in early 90s that if there exists such P (θ), then there always exists a first-degree PPDLM P (θ) = P_{0} + θ P_{1} that meets the desired conditions, regardless of the size or rank of A_{0} and A_{1}. The goal of this paper is to falsify this conjecture. More precisely, we will show a pair of the matrices A_{0}, A_{1} ∈ R^{3 × 3} with A_{0} + θ A_{1} being Hurwitz stable for all θ ∈ [- 1, 1] and prove rigorously that the desired first-degree PPDLM does not exist for this particular pair. The proof is based on the recently developed techniques to deal with parametrized LMIs in an exact fashion and related duality arguments. From this counter-example, we can conclude that the conjecture posed by Barmish is not valid when n ≥ 3 in general.. |

78. |
A Redundant Descriptor Approach to H_∞ State-Feedback Controller Synthesis. |

79. |
Robust H_∞ Performance Analysis of Linear Time-Invariant Uncertain Systems via Polynomially Parameter-Dependent Lyapunov Functions. |

80. |
Stability Analysis for 2-D Discrete Systems. |

81. |
Yoshio Ebihara, Tomomichi Hagiwara, A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems, *Automatica*, 10.1016/j.automatica.2005.05.023, 41, 11, 1933-1941, 2005.11, This paper studies robust performance analysis problems of linear time-invariant systems affected by real parametric uncertainties. In the case where the state-space matrices of the system depend affinely on the uncertain parameters, it is know that recently developed extended or dilated linear matrix inequalities (LMIs) are effective to assess the robust performance in a less conservative fashion. This paper further extends those preceding results and propose a unified way to obtain numerically verifiable dilated LMI conditions even in the case of rational parameter dependence. In particular, it turns out that the proposed dilated LMIs enable us to assess the robust performance via multiaffine parameter-dependent Lyapunov variables so that less conservative analysis results can be achieved. Connections among the proposed conditions and existing results are also discussed concretely. Several existing results can be viewed as particular cases of the proposed conditions.. |

82. |
A Study to Assess the Disturbance Response of Control Systems across Switching. |

83. |
The 16th IFAC World Congress. |

84. |
American Control Conference 2004. |

85. |
Yoshio Ebihara, Tomomichi Hagiwara, New dilated LMI characterizations for continuous-time multiobjective controller synthesis, *Automatica*, 10.1016/j.automatica.2004.06.009, 40, 11, 2003-2009, 2004.11, This paper provides new dilated linear matrix inequality (LMI) characterizations for continuous-time controller synthesis. The dilated LMIs enable us to parametrize controllers without involving the Lyapunov variables in the parametrizations. Taking advantage of this feature, we can readily design multiobjective controllers with non-common Lyapunov variables, whereas we are forced to employ a common one in the well-known Lyapunov shaping paradigm. In particular, it is shown that the proposed dilated-LMI-based approach to H_{2}/D-stability synthesis encompasses the corresponding Lyapunov shaping paradigm as a special case. In this sense, the results of this paper can be viewed as partial counterparts of those obtained in the discrete-time setting.. |

86. |
Yoshio Ebihara, Kazuma Tokuyama, Tomomichi Hagiwara, Structured controller synthesis using LMI and alternating projection method, *International Journal of Control*, 10.1080/00207170412331298947, 77, 12, 1137-1147, 2004.08, In this paper, we propose new LMI-based conditions to design output-feedback controllers under structural constraints. The conditions are represented in terms of LMIs with rank constraints and we apply the alternating projection method to solve them. Even though the alternating projection algorithm does not ensure global convergence, extensive numerical experiments demonstrate that the proposed design method is promising in designing structured controllers. The difficulties and limitations linked with the proposed design method is also discussed.. |

87. |
Yoshio Ebihara, Tomomichi Hagiwara, On H_{∞} model reduction using LMIs, *IEEE Transactions on Automatic Control*, 10.1109/TAC.2004.831116, 49, 7, 1187-1191, 2004.07, In this note, we deal with the problem of approximating a given nth-order linear time-invariant system G by an rth-order system G_{r} where r < n. It is shown that lower bounds of the H_{∞} norm of the associated error system can be analyzed by using linear matrix ineqaulity (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 note provides an alternative proof for those lower bounds via simple algebraic manipulations related to LMIs. 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.. |

88. |
Control System Analysis and Synthesis Using Dilated LMIs. |

89. |
Model Reduction Method Preserving the Steady-State Gain and Its Application to Electric Power Systems. |

90. |
Yoshio Ebihara, Tomomichi Hagiwara, A Dilated LMI Approach to Continuous-Time Gain-Scheduled Controller Synthesis with Parameter-Dependent Lyapunov Variables, *計測自動制御学会論文集*, 39, 8, 734-740, 2003.08. |

91. |
Yoshio Ebihara, Tomomichi Hagiwara, A Dilated LMI Approach to Robust Performance Analysis of Linear Time-Invariant Uncertain Systems, *SICE Annual Conference Program and Abstracts*, 10.11499/sicep.2002.0.569.0, 2002, 0, 569-569, 2002, This paper addresses robust performance analysis problems for linear time-invariant systems depending on uncertain parameters. It is well known that, in the case of affine parameter dependence, we can deal with such problems based on standard LMI (Linear Matrix Inequalities) characterizations and the concept of quadratic stability. However, in the case of rational parameter dependence, we need another effort to arrive at numerically tractable conditions. This paper clarifies that recently developed dilated LMI characterizations are useful in dealing with such robust performance analysis problems. The dilated LMI’s also allow us to employ parameter-dependent Lyapunov variables, which are known to be quite effective to reduce the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable.. |

92. |
Simple Adaptive Control Method with Automatic Tuning of PFC and Its Application to Positioning Control of a Pneumatic Servo System. |

93. |
Yoshio Ebihara, Tomomichi Hagiwara, Mituhiko Araki, Sequential tuning methods of LQ/LQI controllers for multivariable systems and their application to hot strip mills, *International Journal of Control*, 10.1080/002071700445415, 73, 15, 1392-1404, 2000.10, 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. In such tuning, it is desirable to change feedback gains only step by step, confirming that the control performance is actually improved in each step. The first method we propose is such that we design an optimal single-input regulator in each step, by paying attention to only one input of the plant while the feedback laws to other inputs are fixed to those obtained in the previous sequential tuning steps. On the other hand, the second method is such that all elements of the feedback gain are changed at once, while we are given the design freedom about how much we are to change the gain. These two methods as well as their combined use are shown to lead to the optimal gain as a multivariable control system eventually, provided that the sequential tuning steps are repeated sufficiently many times. We apply 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.. |

94. |
A Sequential Tuning Method of Controller based on H_2 Performance. |

95. |
Sequential Tuning Methods for Optimal Control Systems and their Application to Hot Strup Mills. |