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

Guisheng Zhai, Hai Lin, Youngbok Kim

Research output: Contribution to conferencePaper

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
Pages2483-2488
Number of pages6
Publication statusPublished - 2004 Dec 1
Externally publishedYes
EventSICE Annual Conference 2004 - Sapporo, Japan
Duration: 2004 Aug 42004 Aug 6

Conference

ConferenceSICE Annual Conference 2004
CountryJapan
CitySapporo
Period04/8/404/8/6

Keywords

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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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    Zhai, G., Lin, H., & Kim, Y. (2004). 2 gain analysis for switched systems with continuous-time and discrete-time subsystems. 2483-2488. Paper presented at SICE Annual Conference 2004, Sapporo, Japan.