Robust H∞ Vertex-dependent Filtering of State-delayed State-multiplicative Stochastic Systems

Linear state-delayed continuous-time systems with state-multiplicative noise and polytopic type parameter uncertainty are considered. We address the problem of H∞ robust filtering of these systems by applying a vertex dependent Lyapunov function that considerably reduces the over-design that is inherent to the classical design which is based on single Lyapunov function for the whole parameter range. The improved solution is based on the application of the Finsler lemma leading to a unique Lyapunov function that is assigned to each vertex of the polytope uncertainty. An example is given that demonstrates the tractability and applicability of the design methods.