Robust filtering for uncertain linear systems with state-dependent noise

This paper deals with the problems of robust H₂ and H_∞ filtering for a class of linear continuous-time systems subject to uncertain constant parameters and both additive and state-dependent noise signals. The uncertain parameters appear affinely in the matrices of the system state-space model and are assumed to belong to a given polytope. Linear matrix inequality approaches are proposed for designing linear stationary asymptotically stable filters which guarantee an upper-bound on the asymptotic estimation error variance, in the H₂ case, and an upper-bound on the L₂-gain from the additive noise to the estimation error, in the, H_∞case. The results are based on parametric Lyapunov functions.