Delay-dependent filtering for discrete-time systems with finite frequency small gain specifications

This paper is concerned with the delay-dependent filtering problem for linear discrete-time multi-delay systems with small gain conditions in finite frequency ranges. A new multiplier method is developed to convert the resulting non-convex filtering synthesis conditions to the ones based on linear matrix inequalities (LMIs). Thus, sufficient conditions for the existence of feasible filters are given in terms of solutions to a set of LMIs. Finally, the procedures and advantages of the proposed approach in comparison with existing ones in the entire frequency range are illustrated via a numerical example.