Retarded linear systems with stochastic uncertainties — Robust polytopic H∞ static output-feedback control

A linear parameter varying approach for designing a constant output feedback controller for a linear time-invariant retarded system with stochastic multiplicative Wiener-type noise, 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, and in the measurement matrix of the system. The solution of the 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 uncertain case where the system matrices lie within a given polytop.