Improved Robust Stability Criterion for Uncertain Discrete-Time Singular Time-Delay Systems

This paper is concerned with the robust stability problem for uncertain discrete-time singular time-delay systems. By using Jensen inequality, a new sufficient condition is given to ensure a discrete-time singular time-delay to be regular, causal and stable, based on which, a sufficient robust stability criterion for the considered uncertain discrete-time singular time-delay system is given. It should be mentioned that a symmetric matrix in the designed Lyapunov-Krasovskii functional are not confined to be positive definite, which comparatively reduces the conservativeness of this criterion. The obtained results are expressed in terms of linear matrix inequalities (LMIs), which are easy to resolve using the inner point algorithm. Two numerical examples illustrate the less conservativeness of the presented results.