Filtering for a class of discrete-time systems with time-delays via delta operator approach

In this article, a robust H_∞ filtering problem for a class of norm-bounded uncertain discrete-time systems with time delays is investigated using delta operator approach. Based on Lyapunov-Krasovskii functional in delta domain, a new delay-dependent sufficient condition for the solvability of this problem is presented in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an expression of a desired delta operator H_∞ filter is given. The proposed method can unify some previous related continuous and discrete systems into a delta operator systems framework. A numerical example is given to illustrate the effectiveness of the developed techniques.