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

Guisheng Zhai, Ping Xu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

We establish a unified approach to stability and ℒ2 gain 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 stability of all subsystems, then the switched system is stable under arbitrary switching. Furthermore, we show that if there is a common quadratic Lyapunov function for stability and certain ℒ2 gain of all subsystems, then the switched system is stable and has the same ℒ2 gain under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.

Original languageEnglish
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Pages3897-3902
Number of pages6
DOIs
Publication statusPublished - 2009
Externally publishedYes
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai
Duration: 2009 Dec 152009 Dec 18

Other

Other48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
CityShanghai
Period09/12/1509/12/18

Fingerprint

Lyapunov functions
Linear matrix inequalities

Keywords

  • ℒ gain
  • Arbitrary switching
  • Common quadratic Lyapunov functions
  • Linear matrix inequalities (LMIs)
  • Stability
  • Switched linear descriptor systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Zhai, G., & Xu, P. (2009). A unified approach to analysis of switched linear descriptor systems under arbitrary switching. In Proceedings of the IEEE Conference on Decision and Control (pp. 3897-3902). [5400699] https://doi.org/10.1109/CDC.2009.5400699

A unified approach to analysis of switched linear descriptor systems under arbitrary switching. / Zhai, Guisheng; Xu, Ping.

Proceedings of the IEEE Conference on Decision and Control. 2009. p. 3897-3902 5400699.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Zhai, G & Xu, P 2009, A unified approach to analysis of switched linear descriptor systems under arbitrary switching. in Proceedings of the IEEE Conference on Decision and Control., 5400699, pp. 3897-3902, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, 09/12/15. https://doi.org/10.1109/CDC.2009.5400699
Zhai G, Xu P. A unified approach to analysis of switched linear descriptor systems under arbitrary switching. In Proceedings of the IEEE Conference on Decision and Control. 2009. p. 3897-3902. 5400699 https://doi.org/10.1109/CDC.2009.5400699
Zhai, Guisheng ; Xu, Ping. / A unified approach to analysis of switched linear descriptor systems under arbitrary switching. Proceedings of the IEEE Conference on Decision and Control. 2009. pp. 3897-3902
@inproceedings{334453b70c28466bb3cc379e040e5990,
title = "A unified approach to analysis of switched linear descriptor systems under arbitrary switching",
abstract = "We establish a unified approach to stability and ℒ2 gain 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 stability of all subsystems, then the switched system is stable under arbitrary switching. Furthermore, we show that if there is a common quadratic Lyapunov function for stability and certain ℒ2 gain of all subsystems, then the switched system is stable and has the same ℒ2 gain under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.",
keywords = "ℒ gain, Arbitrary switching, Common quadratic Lyapunov functions, Linear matrix inequalities (LMIs), Stability, Switched linear descriptor systems",
author = "Guisheng Zhai and Ping Xu",
year = "2009",
doi = "10.1109/CDC.2009.5400699",
language = "English",
isbn = "9781424438716",
pages = "3897--3902",
booktitle = "Proceedings of the IEEE Conference on Decision and Control",

}

TY - GEN

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

AU - Zhai, Guisheng

AU - Xu, Ping

PY - 2009

Y1 - 2009

N2 - We establish a unified approach to stability and ℒ2 gain 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 stability of all subsystems, then the switched system is stable under arbitrary switching. Furthermore, we show that if there is a common quadratic Lyapunov function for stability and certain ℒ2 gain of all subsystems, then the switched system is stable and has the same ℒ2 gain 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 and ℒ2 gain 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 stability of all subsystems, then the switched system is stable under arbitrary switching. Furthermore, we show that if there is a common quadratic Lyapunov function for stability and certain ℒ2 gain of all subsystems, then the switched system is stable and has the same ℒ2 gain under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.

KW - ℒ gain

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=77950799860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950799860&partnerID=8YFLogxK

U2 - 10.1109/CDC.2009.5400699

DO - 10.1109/CDC.2009.5400699

M3 - Conference contribution

SN - 9781424438716

SP - 3897

EP - 3902

BT - Proceedings of the IEEE Conference on Decision and Control

ER -