Linear discrete- and continuous-time systems with multiplicative noise and polytopic-type parameter uncertainties are considered. The problems of H∞ state-feedback control and filtering of these systems are addressed. These problems are solved by applying a vertex-dependent Lyapunov function, based on the Finsler’s lemma, which considerably reduces the overdesign associated with the classical “quadratic” design that applies a single Lyapunov function for the whole parameters range. In both settings, a cost function is defined which is the expected value of the standard H∞ performance index with respect to the stochastic multiplicative parameters. The results are demonstrated via two numerical examples.