Stability of stochastic discrete-time piecewise homogeneous Markov jump systems with time delay and impulsive effects

This paper considers the stability of stochastic nonlinear discrete-time impulsive systems with time delay and Markov jumps. The transition probabilities of Markov jumps are finite piecewise homogeneous and the variations in the finite set are contingent on a higher-level transition probability matrix. By Lyapunov functional method and the discrete average impulsive interval approach, several novel stability criteria are obtained, which can loosen the constraint on impulsive intervals and thus reduce the conservativeness compared with previous results that take the upper/lower bound of all impulsive intervals. Also, our results are suitable for both stable impulses and unstable impulses. As illustrations, the obtained results are applied to stochastic impulsive neural networks and stochastic impulsive oscillator model, respectively. The simulations are also presented to support and validate the theoretical results.