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

Access to Document

10.2478/v10006-010-0018-2

Fingerprint Dive into the research topics of 'A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching'. Together they form a unique fingerprint.

Cite this

@article{de811fa0036c40a7867820088ef8de9f,

title = "A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching",

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.",

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

author = "Guisheng Zhai and Xuping Xu",

note = "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. Copyright: Copyright 2010 Elsevier B.V., All rights reserved.",

year = "2010",

month = jun,

day = "1",

doi = "10.2478/v10006-010-0018-2",

language = "English",

volume = "20",

pages = "249--259",

journal = "International Journal of Applied Mathematics and Computer Science",

issn = "1641-876X",

publisher = "Walter de Gruyter GmbH",

number = "2",

}

TY - JOUR

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. Copyright: Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2010/6/1

Y1 - 2010/6/1

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.

KW - arbitrary switching

KW - common quadratic Lyapunov functions

KW - linear matrix inequalities (LMIs)

KW - stability

KW - switched linear descriptor systems

UR - http://www.scopus.com/inward/record.url?scp=77954401515&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954401515&partnerID=8YFLogxK

U2 - 10.2478/v10006-010-0018-2

DO - 10.2478/v10006-010-0018-2

M3 - Article

AN - SCOPUS:77954401515

VL - 20

SP - 249

EP - 259

JO - International Journal of Applied Mathematics and Computer Science

JF - International Journal of Applied Mathematics and Computer Science

SN - 1641-876X

IS - 2

ER -