Robust H∞H∞ filter design with past output measurements for uncertain discrete-time systems

This paper is concerned with the design of robust filters for uncertain discrete-time linear systems. The uncertainty is assumed to be time-invariant belonging to a polytope. An upper bound to the H∞H∞ norm of the transfer-function from the system input to the filtering error is used as performance criterion. The novelty is that the resulting robust filter has order greater than the order of the system being filtered by incorporating past output measurements. The design conditions are expressed in terms of convex problems constrained by Linear Matrix Inequalities. Performance is assessed through parameter-dependent Lyapunov functions. The results generalize existing robust filtering procedures without bringing in any additional conservatism. Simple numerical examples illustrate the procedure.