2 gain analysis of switched symmetric systems with time delays

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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we study ℒ2 gain property for a class of switched systems which are composed of a finite number of linear time-invariant (LTI) symmetric subsystems with time delays in system states. We show that when all subsystems have ℒ2 gain γ in the sense of satisfying an LMI, the switched system has the same ℒ2 gain γ under arbitrary switching. The key idea is to establish a common Lyapunov function for all subsystems in the sense of ℒ2 gain.

Original languageEnglish
Pages (from-to)219-232
Number of pages14
JournalDynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Issue number2-3
Publication statusPublished - 2004 Apr 1
Externally publishedYes


  • Arbitrary switching
  • Common Lyapunov function
  • Linear matrix inequality (LMI)
  • Switched symmetric system
  • Time delay
  • ℒ gain

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'ℒ2 gain analysis of switched symmetric systems with time delays'. Together they form a unique fingerprint.

Cite this