A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching

Guisheng Zhai; Xuping Xu

doi:10.2478/v10006-010-0018-2

A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching

Guisheng Zhai, Xuping Xu

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

Abstract

We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switched system is stable under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.

Original language	English
Pages (from-to)	249-259
Number of pages	11
Journal	International Journal of Applied Mathematics and Computer Science
Volume	20
Issue number	2
DOIs	https://doi.org/10.2478/v10006-010-0018-2
Publication status	Published - 2010 Jun 1

Keywords

arbitrary switching
common quadratic Lyapunov functions
linear matrix inequalities (LMIs)
stability
switched linear descriptor systems

ASJC Scopus subject areas

Computer Science (miscellaneous)
Engineering (miscellaneous)
Applied Mathematics

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abstract = "We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switched system is stable under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.",

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T1 - A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching

AU - Zhai, Guisheng

AU - Xu, Xuping

N1 - Funding Information: The authors would like to thank Mr. Ryuuen Kou, Prof. Joe Imae and Prof. Tomoaki Kobayashi of Osaka Prefecture University for valuable discussions. This research has been supported in part by the Japan Ministry of Education, Sciences and Culture under Grants-in-Aid for Scientific Research (C) 21560471.

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N2 - We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switched system is stable under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.

AB - We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switched system is stable under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.

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KW - common quadratic Lyapunov functions

KW - linear matrix inequalities (LMIs)

KW - stability

KW - switched linear descriptor systems

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