Stochastic stability analysis for discrete-time singular Markov jump systems with time-varying delay and piecewise-constant transition probabilities

This paper concerns the stochastic stability analysis for discrete-time singular Markov jump systems with time-varying delay and time-varying transition probabilities. The time-varying transition probabilities in the underlying systems are assumed to be finite piecewise-constant. Based on the delay partitioning technique, a delay-dependent stochastic stability condition is derived for these systems, which is formulated by linear matrix inequalities and thus can be checked easily. Some special cases are also considered. Finally, two numerical examples are provided to demonstrate the application and less conservativeness of the developed approaches.