Delay-dependent robust H∞H∞ filtering for uncertain discrete-time singular systems with interval time-varying delay

This paper focuses on the delay-dependent robust H∞H∞ filtering for uncertain discrete-time singular systems with interval time-varying delay. The uncertainty considered is a convex compact set of polytopic type. The purpose is the design of a linear robust H∞H∞ filter such that the resulting filtering error singular system is regular, causal, and asymptotically stable with a H∞H∞ norm bound. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded real lemma (BRL) for delayed singular systems is derived. Based on the derived BRL, a sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequality (LMI) without decomposing the original system matrices. Also, it is shown that the proposed filter design method is general for both singular systems and non-singular systems. Finally, illustrative examples are presented to show the applicability of the proposed method.