This paper focuses on the problems of stability for positive Markov jump linear systems (PMJLSs) and its application to nonlinear Markov jump stochastic systems (MJSSs). First, we provide sufficient and necessary conditions for $p$-moment exponential stability of PMJLS. Then, based on the proposed results on $p$-moment exponential stability of PMJLS, we obtain explicit stability criteria for nonlinear MJSSs. Finally, two numerical examples are presented to confirm the validity of the obtained theoretical results.

中文翻译：

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正马尔可夫跳线性系统矩稳定的充要条件

本文重点研究正马尔可夫跳跃线性系统（PMJLSs）的稳定性问题及其在非线性马尔可夫跳跃随机系统（MJSSs）中的应用。首先，我们提供充分必要条件$p$-PMJLS 的矩指数稳定性。然后，根据建议的结果$p$-PMJLS 的矩指数稳定性，我们获得了非线性 MJSS 的明确稳定性标准。最后，给出了两个数值例子来验证所获得的理论结果的有效性。