Stochastic H∞ control and estimation of state-multiplicative discrete-time systems with delay

Linear, state delayed, discrete-time systems with stochastic uncertainties in their state-space model are considered. The problems of both H
_∞
state-feedback control and filtering are 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. In both problems, a cost function is defined which is the expected value of the standard H
_∞
performance index with respect to the uncertain parameters.