Delay-range-dependent and delay-distribution-independent stability criteria for discrete-time singular Markovian jump systems

The problem of delay-range-dependent stability for discrete-time singular Markovian jump systems with time-varying delay is discussed in this paper. Based on time-delay partitioning technique, a new delay-range-dependent Lyapunov functional is established firstly. Then, based on the probability idea, LMIs-based delay-range-dependent and delay-distribution-independent conditions are proposed for the system to be regular, causal, and stochastically stable. Furthermore, in terms of solving a set of coupled LMIs, the stabilizing controller is obtained such that the closed-loop system is regular, causal, and stochastically stable. Finally, numerical examples are given to show the results derived from the proposed methods are less conservative than the existing ones.