2 gain analysis for switched systems with continuous-time and discrete-time subsystems

Guisheng Zhai, Hai Lin, Youngbok Kim

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

4 Citations (Scopus)

Abstract

In this paper, we study ℒ2 gain property for a class of switched systems which are composed of both continuous-time LTI subsystems and discrete-time LTI subsystems. Under the assumption that all subsystems are Hurwitz/Schur stable and have the ℒ2 gain less than 7, we discuss the ℒ2 gain that the switched system could achieve. First, we consider the case where a common Lyapunov function exists for all subsystems in ℒ2 sense, and show that the switched system has the ℒ2 gain less than the same level 7 under arbitrary switching. As an example in this case, we analyze switched symmetric systems and derive the common Lyapunov function clearly. Next, we use a piecewise Lyapunov function approach to study the case where no common Lyapunov function exists in ℒ2 sense, and show that the switched system achieves an ultimate (or weighted) ℒ2 gain under an average dwell time scheme.

Original languageEnglish
Title of host publicationProceedings of the SICE Annual Conference
Pages2483-2488
Number of pages6
Publication statusPublished - 2004
Externally publishedYes
EventSICE Annual Conference 2004 - Sapporo
Duration: 2004 Aug 42004 Aug 6

Other

OtherSICE Annual Conference 2004
CitySapporo
Period04/8/404/8/6

Fingerprint

Lyapunov functions

Keywords

  • ℒ gain
  • Average dwell time
  • Common Lyapunov function
  • Piecewise Lyapunov function
  • Switched system

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Zhai, G., Lin, H., & Kim, Y. (2004). 2 gain analysis for switched systems with continuous-time and discrete-time subsystems. In Proceedings of the SICE Annual Conference (pp. 2483-2488). [FPI-10-4]

2 gain analysis for switched systems with continuous-time and discrete-time subsystems. / Zhai, Guisheng; Lin, Hai; Kim, Youngbok.

Proceedings of the SICE Annual Conference. 2004. p. 2483-2488 FPI-10-4.

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

Zhai, G, Lin, H & Kim, Y 2004, 2 gain analysis for switched systems with continuous-time and discrete-time subsystems. in Proceedings of the SICE Annual Conference., FPI-10-4, pp. 2483-2488, SICE Annual Conference 2004, Sapporo, 04/8/4.
Zhai G, Lin H, Kim Y. 2 gain analysis for switched systems with continuous-time and discrete-time subsystems. In Proceedings of the SICE Annual Conference. 2004. p. 2483-2488. FPI-10-4
Zhai, Guisheng ; Lin, Hai ; Kim, Youngbok. / 2 gain analysis for switched systems with continuous-time and discrete-time subsystems. Proceedings of the SICE Annual Conference. 2004. pp. 2483-2488
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