Robust H∞ control and estimation of state-multiplicative stochastic systems with delay

Linear, state delayed, norm bounded uncertain continuous-time systems with stochastic uncertainties in their state-space model are considered. The problems of both H_infin robust state-feedback control and robust filtering are solved, for the stationary case, via an input-output approach by which the system is replaced by a nonretarded system with (additional) deterministic norm-bounded uncertainties. In both problems, a cost function is defined which is the expected value of the standard H_infin performance index with respect to the uncertain parameters. Two examples are given that demonstrate the applicability of the theory.