Stochastic linear systems: Robust H∞ control via vertex-dependent approach

We consider linear continuous-time systems with multiplicative noise and polytopic type parameter uncertainty and we address the problems of H_∞ state-feedback control and filtering of these systems. These problems are solved by applying a vertex dependent Lyapunov function that considerably reduces the over-design associated with the classical “quadratic” design that is based on a single Lyapunov function for the whole parameters range. In both problems, a cost function is defined which is the expected value of the standard H_∞ performance index with respect to the stochastic multiplicative parameters.