Abstract 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.

中文翻译：

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具有时滞和脉冲效应的随机离散时间分段齐次马尔可夫跳跃系统的稳定性

摘要 本文考虑了具有时滞和马尔可夫跳跃的随机非线性离散时间脉冲系统的稳定性。马尔可夫跳跃的转移概率是有限分段齐次的，有限集合中的变化取决于更高级别的转移概率矩阵。通过李雅普诺夫泛函法和离散平均脉冲区间方法，得到了几个新的稳定性判据，与以往取所有脉冲区间的上/下界的结果相比，可以放松对脉冲区间的约束，从而降低保守性。此外，我们的结果适用于稳定脉冲和不稳定脉冲。作为说明，获得的结果分别应用于随机脉冲神经网络和随机脉冲振荡器模型。