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Linear, state delayed, discrete-time systems with stochastic uncertainties in their state-space model are considered. The problems of robust vertex-dependant polytopic H∞ filtering is solved, for the stationary case, via an input-output approach by which the system is replaced by a nonretarded system with deterministic normbounded 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∞ performance index with respect to the uncertain parameters.

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