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 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Pages3897-3902
Number of pages6
DOIs
Publication statusPublished - 2009 Dec 1
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
Duration: 2009 Dec 152009 Dec 18

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Conference

Conference48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
CountryChina
CityShanghai
Period09/12/1509/12/18

Keywords

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

ASJC Scopus subject areas

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

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  • Cite this

    Zhai, G., & Xu, P. (2009). A unified approach to analysis of switched linear descriptor systems under arbitrary switching. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 3897-3902). [5400699] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5400699