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Admissible finite-time stability and stabilization of discrete-time singular systems with time-varying delays

In this paper, a new finite-time stability (FTS) concept, which is defined as admissible finite-time stability (AFTS), is introduced into a class of discrete-time singular systems with time-varying delays. The problems of AFTS analysis and synthesis are addressed. A sufficient condition for the AFTS of the unforced discrete-time singular time-delay system is proposed. Based on the AFTS analysis result, a state feedback controller is designed such that the resulting closed-loop system is admissibly finite-time stable. Both the AFTS and the controller design conditions are provided in terms of a set of linear matrix inequalities (LMIs) with some fixed parameters. Two numerical examples are presented to illustrate the effectiveness of the developed theory.