一类中立型马尔科夫跳跃系统的随机稳定性
Stochastic Stability of a Class of Neutral Markovian Jumping Systems
DOI: 10.12677/AAM.2019.82033, PDF,    科研立项经费支持
作者: 罗 邦, 沈长春, 李 娟, 周守维：贵州民族大学，数据科学与信息工程学院，贵州 贵阳
关键词: 中立型系统；马尔科夫跳跃系统；随机稳定性；Jensen’s不等式；Neutral System； Markovian Jumping Systems； Stochastic Stability； Jensen’s Inequality
摘要: 稳定性是动力系统最重要的性质之一，对解决实际问题具有很重要的理论意义。而时滞的存在是系统性能变差和系统不稳定的根源，故国内外许多专家和学者对其进行研究。本文考虑了一类中立型马尔科夫跳跃系统的随机稳定性问题。首先，通过构造lyapunov函数，利用Ito’s引理和Jensen’s不等式，获得随机稳定性的充分条件。其次，使用matlab中的LMI工具箱，验证结果的正确性。最后，给出两个实例，验证此方法的有效性。
Abstract: Stability is one of the most important properties of dynamical system, which has important theo-retical significance to solve practical problems. The existence of time-delays is the root of system performance difference and systematic instability, so it has been considered by many scientists and scholars at home and abroad. In this paper, the stochastic stability of a class of neutral Markovian jumping systems is considered. Firstly, the Lyapunov function is constructed, and the sufficient conditions of stochastic stability are obtained by using Jensen's inequality. Secondly, the LMI toolbox in Matlab is used to verify the correctness of the results. Finally, two examples are given to verify the validity of this method.
文章引用：罗邦, 沈长春, 李娟, 周守维. 一类中立型马尔科夫跳跃系统的随机稳定性[J]. 应用数学进展, 2019, 8(2): 292-300. https://doi.org/10.12677/AAM.2019.82033

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