马尔可夫跳变非线性系统在离散时间状态下的相关研究
Correlation Study of Discrete Time for Markovian Jump Nonlinear Systems
摘要: 本文主要对离散时间正马尔可夫跳变非线性系统(PMJNS)的随机稳定性进行研究。首先对离散时间正马尔可夫跳变非线性系统随机稳定性的一些定义进行介绍。然后利用多重极大可分Lyapunov函数方法，给出了离散时间正马尔可夫跳变非线性系统的一些随机稳定性判据，以及离散时间正马尔可夫跳变线性系统(PMJLS)的一些相应判据。与以往要求子系统稳定或边缘稳定的结论不同，得到的结果允许一些子系统是不稳定的。基于所提出的准则，离散时间正马尔可夫跳变系统的随机稳定性行为可以由系统函数的代数性质和马尔可夫链的概率特征得到。
Abstract: In this paper, the stochastic stability of discrete-time positive Markovian jump nonlinear systems (PMJNS) is studied. First, some definitions of stochastic stability of discrete-time positive Markovian jump nonlinear systems are introduced. Then, some stochastic stability criteria for discrete-time positive Markovian jump nonlinear systems are given by using the method of multiple maximal separable Lyapunov functions. And some corresponding criteria for discrete-time positive Markovian jump linear systems (PMJLS). Unlike previous conclusions that require subsystem stability or edge stability, the results obtained allow some subsystems to be unstable based on the proposed criteria, the stochastic stability behavior of discrete-time positive Markovian jump systems can be obtained from the algebraic properties of the system functions and the probabilistic characteristics of Markov chains.
文章引用：杨路. 马尔可夫跳变非线性系统在离散时间状态下的相关研究[J]. 理论数学, 2025, 15(4): 14-21. https://doi.org/10.12677/pm.2025.154104

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