Improved stability and stabilization results for discrete singular delay systems via delay partitioning

In this paper, the problems of delay-dependent robust stability analysis and robust stabilization are investigated for uncertain discrete-time singular systems with state delay. First, by making use of the delay partitioning technique, a new delay-dependent criterion is given to ensure the nominal system to be regular, causal and stable. This new criterion is further extended to singular systems with both delay and parameter uncertainties. Moreover, without the assumption that the considered systems being regular and causal, robust controllers are designed for discrete-time singular time-delay systems such that the closed-loop systems have the characteristics of regularity, causality and asymptotic stability. These results are illustrated, via a few numerical examples, to be much less conservative than most of the existing results in the literature.