Stability and L 2 gain analysis for a class of switched symmetric systems

Guisheng Zhai, Xinkai Chen, Masao Ikeda, Kazunori Yasuda

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

26 Citations (Scopus)

Abstract

In this paper, we study stability and L 2 gain properties for a class of switched systems which are composed of a finite number of linear time-invariant symmetric subsystems. We focus our attention mainly on discrete-time systems. When all subsystems are Schur stable, we show that the switched system is exponentially stable under arbitrary switching. Furthermore, we show that when all subsystems are Schur stable and have L 2 gains smaller than a positive scalar γ, the switched system is exponentially stable and has an L 2 gain smaller than the same γ under arbitrary switching. The key idea for both stability and L 2 gain analysis in this paper is to establish a common Lyapunov function for all subsystems in the switched system.

Original languageEnglish
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Pages4395-4400
Number of pages6
Volume4
Publication statusPublished - 2002
Externally publishedYes
Event41st IEEE Conference on Decision and Control - Las Vegas, NV, United States
Duration: 2002 Dec 102002 Dec 13

Other

Other41st IEEE Conference on Decision and Control
CountryUnited States
CityLas Vegas, NV
Period02/12/1002/12/13

Fingerprint

Lyapunov functions

Keywords

  • Arbitrary switching
  • Common lyapunov function
  • Exponential stability
  • L gain
  • Linear matrix inequality (LMI)
  • Switched symmetric system

ASJC Scopus subject areas

  • Chemical Health and Safety
  • Control and Systems Engineering
  • Safety, Risk, Reliability and Quality

Cite this

Zhai, G., Chen, X., Ikeda, M., & Yasuda, K. (2002). Stability and L 2 gain analysis for a class of switched symmetric systems In Proceedings of the IEEE Conference on Decision and Control (Vol. 4, pp. 4395-4400)

Stability and L 2 gain analysis for a class of switched symmetric systems . / Zhai, Guisheng; Chen, Xinkai; Ikeda, Masao; Yasuda, Kazunori.

Proceedings of the IEEE Conference on Decision and Control. Vol. 4 2002. p. 4395-4400.

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

Zhai, G, Chen, X, Ikeda, M & Yasuda, K 2002, Stability and L 2 gain analysis for a class of switched symmetric systems in Proceedings of the IEEE Conference on Decision and Control. vol. 4, pp. 4395-4400, 41st IEEE Conference on Decision and Control, Las Vegas, NV, United States, 02/12/10.
Zhai G, Chen X, Ikeda M, Yasuda K. Stability and L 2 gain analysis for a class of switched symmetric systems In Proceedings of the IEEE Conference on Decision and Control. Vol. 4. 2002. p. 4395-4400
Zhai, Guisheng ; Chen, Xinkai ; Ikeda, Masao ; Yasuda, Kazunori. / Stability and L 2 gain analysis for a class of switched symmetric systems Proceedings of the IEEE Conference on Decision and Control. Vol. 4 2002. pp. 4395-4400
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