Guaranteed cost and filtering for discrete-time polytopic uncertain systems with time delay

The design methods of guaranteed cost filtering and H ∞ filtering for discrete-time uncertain linear systems with time delay are investigated in this paper. The uncertain parameters are assumed to be unknown but belonging to known convex compact set of polytope type less conservative than norm bounded parameter uncertainty. The objective is to design stable guaranteed cost filter and H ∞ filter guaranteeing asymptotic stability for filtering error dynamics and minimizing performance measures. The sufficient conditions for the existence of filters and filter design methods are established by linear matrix inequality (LMI) approach, which can be solved efficiently by so called interior point algorithm. The developed algorithms are illustrated by numerical simulation.