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

Authors:
Emilia Fridman;Michel Dambrine;Nima Yeganefar
Affiliations:
Department of Electrical Engineering Systems, School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel;LAMIH UMR CNRS-UVHC 8530, Valenciennes University, 59313 Valenciennes cedex 9, France;LAGIS CNRS UMR 8146, Ecole Centrale de Lille, 59651 Villeneuve d'Ascq cedex, France
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

Nonlinear matrix inequalities (NLMIs) approach, which is known to be efficient for stability and L"2-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.