离散马尔可夫跳跃线性奇异系统的稳定性分析
Stability Analysis of Discrete-Time Markovian Jump Linear Singular Systems
摘要: 在本文中，我们提出了具有部分已知转移概率的马尔可夫跳跃线性奇异系统(MJLSS)概率渐近稳定性的充分条件。为了解决这个问题，提供了所考虑系统的概率渐近稳定性的随机李雅普诺夫定理。此外，我们还证明了原始系统与其基于奇异值分解的差分代数形式具有相同的稳定性。通过利用先前文献的早期结果，获得了线性矩阵不等式的充分条件。最后，给出了相关算例以证明所提出的稳定性分析的有效性。
Abstract: In this paper, we present sufficient conditions for the Asymptotic stability in probability of a Markovian jump linear singular system (MJLSS) with partially known transition probabilities. To handle this problem, a stochastic Lyapunov theorem on asymptotic stability in probability for the considered systems is provided. Also, we show that the original system has the same stability property as its difference-algebraic form based on singular value decomposition. By utilizing the earlier results on previous literatures, a sufficient condition is obtained in terms of linear matrix inequalities. Finally, relevant examples are presented in order to show the effectiveness of the proposed stability analysis.
文章引用：陈柏江, 叶志勇. 离散马尔可夫跳跃线性奇异系统的稳定性分析[J]. 应用数学进展, 2025, 14(3): 398-408. https://doi.org/10.12677/aam.2025.143127

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