On characterizations of the input-to-state stability property

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We show that the well-known Lyapunov sufficient condition for "input-to-state stability" (ISS) is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.

Original languageEnglish (US)
Pages (from-to)351-359
Number of pages9
JournalSystems and Control Letters
Issue number5
StatePublished - Apr 10 1995

All Science Journal Classification (ASJC) codes

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


  • Input/state stability
  • Lyapunov function techniques
  • Nonlinear stability

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