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

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.