Common Lyapunov functions for families of commuting nonlinear systems

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We present constructions of a local and global common Lyapunov function for a finite family of pairwise commuting globally asymptotically stable nonlinear systems. The constructions are based on an iterative procedure, which at each step invokes a converse Lyapunov theorem for one of the individual systems. Our results extend a previously available one which relies on exponential stability of the vector fields.

Original languageEnglish (US)
Pages (from-to)405-416
Number of pages12
JournalSystems and Control Letters
Issue number5
StatePublished - May 2005


  • Common Lyapunov functions
  • Commutativity
  • Switched nonlinear systems
  • Uniform asymptotic stability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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