Stochastic H∞ Static output-feedback control of state-multiplicative discrete-time systems with delay

We consider linear state-delayed discrete-time systems with stochastic uncertainties in their state-space model. The problem of H_∞ static output-feedback control is solved, for the stationary case, via the input-output approach by which 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 nominal and uncertain polytopic systems, where for the former, a single LMI is obtained and where in the latter a quadratic and a vertex-dependent approach are adopted. 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. A numerical example is given that demonstrates the applicability and tractability of the theory.