| 王刚，吴小太.带Markov切换的随机微分系统的输入状态稳定性[J].重庆工商大学学报（自然科学版）,2019,36(1):1-5 |
| 带Markov切换的随机微分系统的输入状态稳定性 |
| Input-to-state Stability of Stochastic Differential System with Markov Switching |
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| DOI： |
| 中文关键词: Markov切换 随机微分系统 输入状态稳定 |
| 英文关键词:Markov switching stochastic differential system input-to-state stabilization |
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| 摘要点击次数: 416 |
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| 中文摘要: |
| 针对一类具有外部输入的非线性随机微分系统，研究了带Markov切换的随机微分系统的输入状态稳定性问题；首先，引入了一种马氏链遍历性定义，基于该定义提出了一类分析带Markov切换的随机微分系统输入状态稳定性的新方法；然后，借助Lyapunov-Krasovskii函数方法，将随机微分系统的状态划分为两种情况，针对这两种不同的情况，分别讨论了在外部输入量影响下系统状态的有界性，进而得出该非线性带Markov切换随机微分系统输入状态的稳定性。 |
| 英文摘要: |
| For a class of nonlinear stochastic differential systems with external input，we have studied the problem of input to state stability analysis of stochastic differential systems with Markov switching.First of all，we introduced a definition of ergodic property for Markov chain. Based on this definition，a new method to analyze the input-to-state stability of a stochastic differential system with Markov switching is proposed.Then，by using Lyapunov-Krasovskii function method，the state of stochastic differential system is divided into two cases. For these two cases，we discussed the boundedness of system state under the influence of external input.At last，the input to state stability of the nonlinear switched stochastic differential system with Markov switching is obtained. |
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