On <i>ℋ︁</i><sub>∞</sub> model reduction for discrete‐time linear time‐invariant systems using linear matrix inequalities

Ebihara, Yoshio; Hirai, Yoshito; Hagiwara, Tomomichi

doi:10.1002/asjc.35

Cited by 7 publications

(5 citation statements)

References 25 publications

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“…In [8], [9], we have shown that the well-known H ∞ norm bounds in model order reduction can be reproduced by LMIs. The current study inherits the basic spirit of [8], [9].…”

Section: Introductionmentioning

confidence: 90%

LMI-Based Lower Bound Analysis of the Best Achievable H∞ Performance for SISO Systems

Ebihara

Matsuo

Hagiwara

2016

SICE Journal of Control, Measurement, and System Integration

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: 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.

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“…In [8], [9], we have shown that the well-known H ∞ norm bounds in model order reduction can be reproduced by LMIs. The current study inherits the basic spirit of [8], [9].…”

Section: Introductionmentioning

confidence: 90%

LMI-Based Lower Bound Analysis of the Best Achievable H∞ Performance for SISO Systems

Ebihara

Matsuo

Hagiwara

2016

SICE Journal of Control, Measurement, and System Integration

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“…Therefore, from a control theoretic viewpoint, it is intriguing if we can obtain analytical results on the best achievable H ∞ performance limitations by means of LMIs. In [5], [6], we have shown that the well-known H ∞ norm bounds in model order reduction can be reproduced by LMIs. The current study inherits the basic spirit of [5], [6].…”

Section: Introductionmentioning

confidence: 97%

“…In [5], [6], we have shown that the well-known H ∞ norm bounds in model order reduction can be reproduced by LMIs. The current study inherits the basic spirit of [5], [6].…”

Section: Introductionmentioning

confidence: 97%

H<inf>∞</inf> performance limitations analysis for SISO systems: A dual LMI approach

Ebihara

Waki

Sebe

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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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+ P K) −1 P 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.

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“…The standard H• model reduction problem for integer order systems has been extensively investigated in recent decades [1][2][3][4][5][6][7], and positivity-preserving H• model reduction for positive systems has also attracted some attention [8][9][10]. Nevertheless, their counterparts for fractional order systems are still not well-developed.…”

Section: Introductionmentioning

confidence: 99%

H_∞ Model Reduction for Positive Fractional Order Systems

Shen¹,

Lam²

2013

Asian Journal of Control

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This paper focuses on the H• model reduction problem of positive fractional order systems. For a stable positive fractional order system, we aim to construct a positive reduced-order fractional system such that the associated error system is stable with a prescribed H• performance. Then, based on the bounded real lemma for fractional order systems, a sufficient condition is given to characterize the model reduction problem with a prescribed H•-norm error bound in terms of a linear matrix inequality (LMI). Furthermore, by introducing a new flexible real matrix variable, the desired reduced-order system matrices are decoupled with the complex matrix variable and further parameterized by the new matrix variable. A corresponding iterative LMI algorithm is also proposed. Finally, several illustrative examples are given to show the effectiveness of the proposed algorithms.

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On ℋ︁_∞ model reduction for discrete‐time linear time‐invariant systems using linear matrix inequalities

Cited by 7 publications

References 25 publications

LMI-Based Lower Bound Analysis of the Best Achievable H∞ Performance for SISO Systems

LMI-Based Lower Bound Analysis of the Best Achievable H∞ Performance for SISO Systems

H<inf>∞</inf> performance limitations analysis for SISO systems: A dual LMI approach

H_∞ Model Reduction for Positive Fractional Order Systems

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On ℋ︁∞ model reduction for discrete‐time linear time‐invariant systems using linear matrix inequalities

Cited by 7 publications

References 25 publications

LMI-Based Lower Bound Analysis of the Best Achievable H&infin; Performance for SISO Systems

LMI-Based Lower Bound Analysis of the Best Achievable H&infin; Performance for SISO Systems

H<inf>∞</inf> performance limitations analysis for SISO systems: A dual LMI approach

H∞ Model Reduction for Positive Fractional Order Systems

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Product

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On ℋ︁_∞ model reduction for discrete‐time linear time‐invariant systems using linear matrix inequalities

LMI-Based Lower Bound Analysis of the Best Achievable H∞ Performance for SISO Systems

LMI-Based Lower Bound Analysis of the Best Achievable H∞ Performance for SISO Systems

H_∞ Model Reduction for Positive Fractional Order Systems