On input-to-state stability of systems with time-delay: A matrix inequalities approach

Emilia Fridman, Michel Dambrine, Nima Yeganefar

Research output: Contribution to journalArticlepeer-review

Abstract

Nonlinear matrix inequalities (NLMIs) approach, which is known to be efficient for stability and L2-gain analysis, is extended to input-to-state stability (ISS). We first obtain sufficient conditions for ISS of systems with time-varying delays via Lyapunov-Krasovskii method. NLMIs are derived then for a class of systems with delayed state-feedback by using the S-procedure. If NLMIs are feasible for all x, then the results are global. When NLMIs are feasible in a compact set containing the origin, bounds on the initial state and on the disturbance are given, which lead to bounded solutions. The numerical examples of sampled-data quantized stabilization illustrate the efficiency of the method.

Original languageEnglish
Pages (from-to)2364-2369
Number of pages6
JournalAutomatica
Volume44
Issue number9
DOIs
StatePublished - Sep 2008

Keywords

  • Input-to-state stability
  • LMI
  • Lyapunov-Krasovskii method
  • Time-delay systems

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