一类中立型Markovian跳跃系统的渐近稳定性
Asymptotic Stability of a Class of Neutral Markovian Jump Systems
DOI: 10.12677/AAM.2019.83060, PDF,    科研立项经费支持
作者: 罗 邦, 沈长春, 周守维, 李 娟：贵州民族大学数据科学与信息工程学院，贵州 贵阳
关键词: 李雅普诺夫；渐近稳定性；Markovian；Jensen’s不等式；Lyapunov； Asymptotic Stability； Markovian； 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，故引起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Markovian跳跃系统的渐近稳定性问题。首先，构造李雅普诺夫函数，利用Ito’s引理和Jensen’s不等式，获得渐近稳定性的条件。其次，使用MATLAB中的LMI工具箱，验证结果的正确性。最后，列举两个实例，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 asymptotic stability of a class of neutral Markovian jump systems is considered. Firstly, the Lyapunov function is constructed and the conditions for asymptotic stability are obtained by using Ito’s lemma and 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 the method.
文章引用：罗邦, 沈长春, 周守维, 李娟. 一类中立型Markovian跳跃系统的渐近稳定性[J]. 应用数学进展, 2019, 8(3): 540-549. https://doi.org/10.12677/AAM.2019.83060

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