一类中立型马尔科夫跳跃系统的稳定性分析
Stability Analysis of a Class of Neutral Markov Jump Systems
DOI: 10.12677/DSC.2019.84027, PDF,    科研立项经费支持
作者: 李 娟, 沈长春：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；Jensen’s不等式；Wirtinger-Based不等式；Neutral System； Markovian Jump Systems； Jensen’s Inequality； Wirtinger-Based Inequality
摘要: 本文研究了具有部分转移概率信息的中立型马尔科夫跳跃系统的稳定性问题，讨论的是具有时变时滞的跳跃系统。首先，构造新的李雅谱诺夫泛函，利用Jensen’s不等式和Wirtinger-based不等式等矩阵不等式分析技巧，并引入相应的自由权矩阵，得到具有时变时滞系统的稳定性条件。其次，利用Matlab中的LMI控制工具箱对所得线性矩阵不等式进行验证。最后，给出三个数值算例，证明所得结果的有效性。
Abstract: This paper addresses the problem of the delay-dependent stability for neutral Markovian jump systems with partial information on transition probability. The time delays discussed in this paper are time-varying delays. Firstly, to obtain the stability condition of the system with time-varying delays, the newly constructed Lyapunov function is combined with Jensen’s inequality and Wirt-inger-based inequality by using the analysis technique of matrix inequalities and the corresponding free weight matrix. Secondly, the obtained results are formulated in terms of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Finally, three numerical examples are given to show the validity and potential of the developed criteria.
文章引用：李娟, 沈长春. 一类中立型马尔科夫跳跃系统的稳定性分析[J]. 动力系统与控制, 2019, 8(4): 248-262. https://doi.org/10.12677/DSC.2019.84027

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