Robust H_∞ and l₂-l_∞, filtering for discrete time-delay systems with nonlinear disturbances

This paper investigates the problem of robust H_∞ and l₂-l_∞ filtering for a class of uncertain nonlinear discrete-time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope and the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H_∞ or l₂-l _∞ sense with respect to all energy-bounded noise disturbances for all admissible uncertainties and time delays. Sufficient conditions for the existence of such filters are formulated in terms of a couple of linear matrix inequalities (LMIs), upon which admissible filters can be obtained from the solution of convex optimization problems. A numerical example is presented to illustrate the feasibility of the developed filter design methods.