The almost surely (a.s.) exponential stability is studied for semi-Markovian switched stochastic systems with randomly impulsive jumps. We start from the case that switches and impulses occur synchronously, in which the impulsive switching signal is a semi-Markovian process. For the case that switches and impulses occur asynchronously, the impulsive arrival time sequence and the types of jump maps are driven by a renewal process and a Markov chain, respectively. By applying the multiple Lyapunov function approach, sufficient conditions of exponential stability a.s. are obtained based upon the ergodic property of semi-Markovian process. The validity of the proposed theoretical results is demonstrated by a numerical example.

研究了具有随机脉冲跳跃的半马尔可夫切换随机系统的几乎肯定的（as）指数稳定性。我们从开关和脉冲同步发生的情况开始，其中脉冲开关信号是一个半马尔可夫过程。对于开关和脉冲异步发生的情况，脉冲到达时间序列和跳跃图的类型分别由更新过程和马尔可夫链驱动。通过应用多重李雅普诺夫函数方法，基于半马尔可夫过程的遍历性质，获得了足够的指数稳定性条件。数值算例证明了所提出理论结果的有效性。