Abstract In this paper, we are concerned with stochastic stability of nonlinear positive systems with random switching signals. The random switching signals are triggered by a stochastic process which is independent of the state of the system. Our results provide sufficient conditions on global asymptotic stability in stochastic sense for nonlinear positive systems when individual subsystems are stable and a certain slow switching condition holds. This slow switching condition takes the form of an asymptotic upper bound on the non-homogeneous probability mass function of the number of switches that occur between the initial and current time instants. Due to the “non-homogeneousness”, the non-homogeneous Poisson process and semi-Markov process are included to generate the switching signals. Simulation example verifies the validity of our results.

中文翻译：

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具有随机开关信号的非线性正系统的随机稳定性

摘要 在本文中，我们关注具有随机开关信号的非线性正系统的随机稳定性。随机开关信号由与系统状态无关的随机过程触发。我们的结果为非线性正系统在随机意义上的全局渐近稳定性提供了充分条件，当单个子系统稳定并且某个慢速切换条件成立时。这种缓慢切换条件采用在初始和当前时刻之间发生的切换次数的非齐次概率质量函数的渐近上限的形式。由于“非齐次性”，包括非齐次泊松过程和半马尔可夫过程来产生开关信号。仿真实例验证了我们结果的有效性。