Retarded linear systems with stochastic uncertainties - Robust reduced-order H∞ output-feedback control

In this paper a method for designing a reduced-order output feedback controller for a linear time-invariant retarded system with stochastic state-multiplicative Wiener-type noise, that achieves a minimum bound on the H_∞ performance level, is introduced. The solution of the stochastic H_∞ reduced-order 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. The stochastic uncertainties appear in the dynamic matrices, which correspond to the delayed and non-delayed states of the system. 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. The results achieved for the nominal case are extended to the case where the system matrices reside in a given polytope.