A note on multiple lyapunov functions and stability condition for switched and hybrid systems

Guisheng Zhai, Isatada Matsune, Joe Imae, Tomoaki Kobayashi

Research output: Contribution to journalArticle

29 Citations (Scopus)


In this note, we consider stability condition with multiple Lyapunov functions for switched and hybrid systems. By using the idea of evaluating "the average value of multiple Lyapunov functions" during the activation interval of each subsystem, we propose a new Lyapunov stability condition, which complements the existing stability conditions that evaluate the value of multiple Lyapunov functions at the starting points or the ending points. We present several demonstrative examples, including the case where unstable subsystems are involved, and also apply the stability condition and the switching strategy to the switching control problem for stabilization of nonholonomic systems.

Original languageEnglish
Pages (from-to)1189-1199
Number of pages11
JournalInternational Journal of Innovative Computing, Information and Control
Issue number5
Publication statusPublished - 2009 May
Externally publishedYes



  • Average value of multiple lyapunov functions
  • Lyapunov stability
  • Multiple Lyapunov functions
  • Nonholonomic systems
  • Switched and hybrid systems
  • Switching strategy

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Information Systems
  • Software
  • Theoretical Computer Science

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