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.