Analysis and design of switched normal systems

Guisheng Zhai, Xuping Xu, Hai Lin, Anthony N. Michel

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.

Original languageEnglish
Pages (from-to)2248-2259
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number12
Publication statusPublished - 2006 Dec 15
Externally publishedYes


  • Activation time ratio between stable and unstable subsystems
  • Arbitrary switching
  • Common Lyapunov function
  • Stability
  • Switched normal system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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