Robust Vertex-dependant H∞ Filtering of Stochastic Discrete-time Systems with Delay

Linear, state delayed, discrete-time systems with stochastic uncertainties in their state-space model are considered. The problems of robust vertex-dependant polytopic H-infinity filtering is solved, for the stationary case, via an input-output approach by which the system is replaced by a nonretarded system with deterministic norm-bounded uncertainties. A vertex-dependent solution is obtained by applying a modified version of the Finsler lemma In this problem, a cost function is defined which is the expected value of the standard H-infinity performance index with respect to the uncertain parameters.