$H_\infty$ Control and Estimation of Retarded State-Multiplicative Stochastic Systems

Linear, state-delayed, continuous-time systems with stochastic uncertainties in their state-space model are considered. The problems of both H_infin 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 that is the expected value of the standard H_infin performance index with respect to the uncertain parameters. Three examples are given that demonstrate the applicability of the theory.