Stability and ℒ 2 Gain Analysis for Switched Symmetric Systems with Time Delay

Guisheng Zhai, Ye Sun, Xinkai Chen, Anthony N. Michel

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

70 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 systems with time delay. We show that when all subsystems are asymptotically stable in the sense of satisfying an LMI, the switched system is asymptotically stable under arbitrary switching. Furthermore, we show that when all subsystems are asymptotically stable and have the ℒ 2 gains γ in the sense of satisfying an LMI, the switched system is asymptotically stable and has the same ℒ 2 gain 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 American Control Conference
Pages2682-2687
Number of pages6
Volume3
Publication statusPublished - 2003
Externally publishedYes
Event2003 American Control Conference - Denver, CO, United States
Duration: 2003 Jun 42003 Jun 6

Other

Other2003 American Control Conference
CountryUnited States
CityDenver, CO
Period03/6/403/6/6

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Time delay
Lyapunov functions

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Zhai, G., Sun, Y., Chen, X., & Michel, A. N. (2003). Stability and ℒ 2 Gain Analysis for Switched Symmetric Systems with Time Delay In Proceedings of the American Control Conference (Vol. 3, pp. 2682-2687)

Stability and ℒ 2 Gain Analysis for Switched Symmetric Systems with Time Delay . / Zhai, Guisheng; Sun, Ye; Chen, Xinkai; Michel, Anthony N.

Proceedings of the American Control Conference. Vol. 3 2003. p. 2682-2687.

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

Zhai, G, Sun, Y, Chen, X & Michel, AN 2003, Stability and ℒ 2 Gain Analysis for Switched Symmetric Systems with Time Delay in Proceedings of the American Control Conference. vol. 3, pp. 2682-2687, 2003 American Control Conference, Denver, CO, United States, 03/6/4.
Zhai G, Sun Y, Chen X, Michel AN. Stability and ℒ 2 Gain Analysis for Switched Symmetric Systems with Time Delay In Proceedings of the American Control Conference. Vol. 3. 2003. p. 2682-2687
Zhai, Guisheng ; Sun, Ye ; Chen, Xinkai ; Michel, Anthony N. / Stability and ℒ 2 Gain Analysis for Switched Symmetric Systems with Time Delay Proceedings of the American Control Conference. Vol. 3 2003. pp. 2682-2687
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