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H Control and Estimation of State-Multiplicative Stochastic Systems with Delay

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