Robust sliding-mode filtering for a class of uncertain nonlinear time-delay systems

This paper is concerned with the problems of robust sliding mode filter designs for a class of nonlinear systems with parameter uncertainties and time-vary delays. The nonlinearities are assumed to satisfy global Lipschitz conditions and parameter uncertainties reside in a polytope. The resulting filter is of the Luenberger type with discontinuous form, it guarantees the robust asymptotic stability of the filtering error dynamics for all admissible uncertainties. A sufficient condition with delay-dependent is given for the existence of such a filter in terms of linear matrix inequalities (LMIs). The resulting filter can be easily obtained from the optimal solutions of this set of LMIs.