Analysis of switched normal discrete-time systems

Guisheng Zhai, Hai Lin, Xuping Xu, Joe Imae, Tomoaki Kobayashi

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


In this paper, we study stability and L2 gain properties for a class of switched systems which are composed of normal discrete-time subsystems. When all subsystems are Schur stable, we show that a common quadratic Lyapunov function exists for all subsystems and that the switched normal system is exponentially stable under arbitrary switching. For L2 gain analysis, we introduce an expanded matrix including each subsystem's coefficient matrices. Then, we show that if the expanded matrix is normal and Schur stable so that each subsystem is Schur stable and has unity L2 gain, then the switched normal system also has unity L2 gain under arbitrary switching. The key point is establishing a common quadratic Lyapunov function for all subsystems in the sense of unity L2 gain.

Original languageEnglish
Pages (from-to)1788-1799
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number8
Publication statusPublished - 2007 Apr 15
Externally publishedYes


  • Common quadratic Lyapunov functions
  • L gain
  • LMI
  • Stability
  • Switched normal systems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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