Static H₂ and H_∞ output-feedback of linear systems with stochastic uncertainties

A linear parameter dependent approach for designing a constant output feedback controller for a linear time-invariant system with stochastic multiplicative Wiener-type noise is introduced, that achieves a minimum bound on either the stochastic H₂ or the H_∞ performance level. A solution is achieved also for the case where in addition to the stochastic parameters, the system matrices reside in a given polytope. In this case, a parameter dependent Lyapunov function is introduced which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope. The stochastic uncertainties appear in both the dynamic and the measurement matrices of the system. The problems are solved using the expected value of the standard performance index over the stochastic parameters.