Static Output-Feedback Control of Retarded Stochastic Systems

Linear, state-delayed, discrete-time systems with stochastic uncertainties in their state-space model are considered. The problem of H_∞ static output-feedback control is solved, for the stationary case, via the input–output approach where the system is replaced by a non-retarded system with deterministic norm-bounded uncertainties. Based on the BRL result of the above systems, solutions are obtained for the nominal and the uncertain polytopic cases where, for the former, a single linear matrix inequality solution is obtained and where, in the latter case, quadratic, less conservative, vertex-dependent approaches are adopted. A numerical example is given that demonstrates the applicability and tractability of the theory.