Robust Norm-Bounded H∞ Static Output-Feedback Control of Retarded Stochastic Systems

An input-output approach for designing a constant output feedback controller for a linear time-invariant retarded system with stochastic state-multiplicative white noise sequences, that achieves a minimum bound on the H performance level is introduced. The stochastic uncertainties appear in the dynamic matrices, which correspond to the delayed and non-delayed states of the system. The solution of the robust norm-bounded H static output-feedback control problem is solved, for the stationary case, via the input-output approach where the system is replaced by a non-retarded system that contain, instead, deterministic norm-bounded uncertainties. In this problem, a cost function is defined which is the expected value of the standard H performance cost with respect to the stochastic parameters. We extend the results achieved for the nominal case, to the case where the system matrices contain norm bounded uncertainties.