An LMI approach to ℒ2 gain analysis and control synthesis of switched systems

Dongmei Xie; Long Wang; Guangming Xie; Fei Hao

An LMI approach to ℒ₂ gain analysis and control synthesis of switched systems

Dongmei Xie^*
, Long Wang
, Guangming Xie
, Fei Hao

^*Corresponding author for this work

Peking University
Tianjin University

Research output: Contribution to conference › Paper › peer-review

7 Scopus citations

Abstract

This paper investigates the ℒ₂ gain analysis and control synthesis of discrete-time switched systems under arbitrary switching by linear matrix inequality (LMI) approach together with switched Lyapunov function method. First, The existence of a switched Lyapunov function is proven to be equivalent to the feasibility of some LMIs. An upper bound of the ℒ₂ gain for switched systems can be computed by solving an eigenvalue problem (EVP). Then, we design a switched state feedback controller and a switched output feedback controller, respectively, guaranteeing that the corresponding closed-loop system is asymptotically stable with an ℒ₂ gain smaller than a fixed constant. LMI-based conditions for both cases are presented. Finally, two examples are given to illustrate our results.

Original language	English
Pages	350-355
Number of pages	6
State	Published - 2004
Externally published	Yes
Event	2004 IEEE International Symposium on Computer Aided Control System Design - Taipei, Taiwan, Province of China Duration: 2 Sep 2004 → 4 Sep 2004

Conference

Conference	2004 IEEE International Symposium on Computer Aided Control System Design
Country/Territory	Taiwan, Province of China
City	Taipei
Period	2/09/04 → 4/09/04

Cite this

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title = "An LMI approach to ℒ2 gain analysis and control synthesis of switched systems",

abstract = "This paper investigates the ℒ2 gain analysis and control synthesis of discrete-time switched systems under arbitrary switching by linear matrix inequality (LMI) approach together with switched Lyapunov function method. First, The existence of a switched Lyapunov function is proven to be equivalent to the feasibility of some LMIs. An upper bound of the ℒ2 gain for switched systems can be computed by solving an eigenvalue problem (EVP). Then, we design a switched state feedback controller and a switched output feedback controller, respectively, guaranteeing that the corresponding closed-loop system is asymptotically stable with an ℒ2 gain smaller than a fixed constant. LMI-based conditions for both cases are presented. Finally, two examples are given to illustrate our results.",

author = "Dongmei Xie and Long Wang and Guangming Xie and Fei Hao",

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note = "2004 IEEE International Symposium on Computer Aided Control System Design ; Conference date: 02-09-2004 Through 04-09-2004",

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T1 - An LMI approach to ℒ2 gain analysis and control synthesis of switched systems

AU - Xie, Dongmei

AU - Wang, Long

AU - Xie, Guangming

AU - Hao, Fei

PY - 2004

Y1 - 2004

N2 - This paper investigates the ℒ2 gain analysis and control synthesis of discrete-time switched systems under arbitrary switching by linear matrix inequality (LMI) approach together with switched Lyapunov function method. First, The existence of a switched Lyapunov function is proven to be equivalent to the feasibility of some LMIs. An upper bound of the ℒ2 gain for switched systems can be computed by solving an eigenvalue problem (EVP). Then, we design a switched state feedback controller and a switched output feedback controller, respectively, guaranteeing that the corresponding closed-loop system is asymptotically stable with an ℒ2 gain smaller than a fixed constant. LMI-based conditions for both cases are presented. Finally, two examples are given to illustrate our results.

AB - This paper investigates the ℒ2 gain analysis and control synthesis of discrete-time switched systems under arbitrary switching by linear matrix inequality (LMI) approach together with switched Lyapunov function method. First, The existence of a switched Lyapunov function is proven to be equivalent to the feasibility of some LMIs. An upper bound of the ℒ2 gain for switched systems can be computed by solving an eigenvalue problem (EVP). Then, we design a switched state feedback controller and a switched output feedback controller, respectively, guaranteeing that the corresponding closed-loop system is asymptotically stable with an ℒ2 gain smaller than a fixed constant. LMI-based conditions for both cases are presented. Finally, two examples are given to illustrate our results.

UR - https://www.scopus.com/pages/publications/20344404703

M3 - 论文

AN - SCOPUS:20344404703

SP - 350

EP - 355

T2 - 2004 IEEE International Symposium on Computer Aided Control System Design

Y2 - 2 September 2004 through 4 September 2004

ER -

An LMI approach to ℒ₂ gain analysis and control synthesis of switched systems

Abstract

Conference

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