LMI approach to robust filtering for discrete time-delay systems with nonlinear disturbances

This paper investigates the problem of robust 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 that 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. Both delay-dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays.