Stabilization of discrete time-varying delay systems: A convex parameter dependent approach

A parameter dependent Lyapunov-Krasovskii based approach is developed to deal with robust stability analysis as well as with the robust stabilization of discrete time-varying systems with time-varying delay. It uses a polytopic representation of uncertainties which can affect dynamic and control matrices. Both robust analysis conditions and synthesis of robust state feedback gains conditions are presented as simple convex feasibility tests. Some numerical examples are presented to illustrate the efficacy of the proposed LMI conditions.