Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems

Guisheng Zhai, Derong Liu, Joe Imae, Tomoaki Kobayashi

Research output: Contribution to journalArticle

58 Citations (Scopus)


We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all continuous-time subsystems are Hurwitz stable, all discrete-time subsystems are Schur stable, and furthermore the obtained Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. A numerical example is provided to demonstrate the result.

Original languageEnglish
Pages (from-to)152-156
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Issue number2
Publication statusPublished - 2006 Feb
Externally publishedYes



  • Arbitrary switching
  • Common quadratic Lyapunov functions
  • Continuous-time
  • Dicrete-time
  • Exponential stability
  • Lie algebra
  • Switched systems

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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