Stability and L2 gain analysis for a class of switched symmetric systems

Guisheng Zhai, Xinkai Chen, Masao Ikeda, Kazunori Yasuda

Research output: Contribution to journalConference article

26 Citations (Scopus)


In this paper, we study stability and L2 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 L2 gains smaller than a positive scalar γ, the switched system is exponentially stable and has an L2 gain smaller than the same γ under arbitrary switching. The key idea for both stability and L2 gain analysis in this paper is to establish a common Lyapunov function for all subsystems in the switched system.

Original languageEnglish
Pages (from-to)4395-4400
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Publication statusPublished - 2002 Dec 1
Event41st IEEE Conference on Decision and Control - Las Vegas, NV, United States
Duration: 2002 Dec 102002 Dec 13



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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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