Stabilization of stochastic nonlinear semi-Markov jump systems via aperiodic intermittent feedback control

IF 4.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2025-05-29 DOI:10.1016/j.jfranklin.2025.107749

Dalin Zhu, Quanxin Zhu

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引用次数: 0

Abstract

In this paper, the almost sure exponential stability (ASES) for a class of stochastic nonlinear semi-Markov jump systems characterized by a random switching process is investigated. By comprehensively utilizing Takagi–Sugeno (T-S) fuzzy strategies, the semi-Markov jump T-S fuzzy systems (SMJT-SFSs) are established. Besides, we set a novel mode-dependent aperiodic intermittent state feedback control. Based on a new form of the multiple-coupled Lyapunov function and the ergodic property of the random switching for semi-Markov process, the sufficient stability conditions for SMJT-SFSs are derived in terms of solvable forms about linear matrix inequalities (LMIs). In particular, our results indicate that the whole semi-Markov jump system can be calmed by designing a novel control with mode dependent intermittent state feedback control even if all subsystems are unstable. Finally, a numerical example and an application example involving a nonlinear double-link robot arm model is presented to illustrate and validate the theoretical results.

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随机非线性半马尔可夫跳变系统的非周期间歇反馈镇定

研究了一类具有随机切换过程的随机非线性半马尔可夫跳变系统的指数稳定性问题。综合利用Takagi-Sugeno （T-S）模糊策略，建立了半马尔可夫跳跃T-S模糊系统（SMJT-SFSs）。此外，我们还建立了一种新的依赖于模式的非周期间歇状态反馈控制。基于多耦合Lyapunov函数的一种新形式和半马尔可夫过程随机切换的遍历性，用线性矩阵不等式的可解形式导出了SMJT-SFSs的充分稳定性条件。特别是，我们的研究结果表明，即使所有子系统都不稳定，也可以通过设计一种具有模式相关间歇状态反馈控制的新型控制来平静整个半马尔可夫跳变系统。最后，给出了一个非线性双连杆机械臂模型的数值算例和应用实例，对理论结果进行了验证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of The Franklin Institute-engineering and Applied Mathematics 工程技术-工程：电子与电气

CiteScore

7.30

自引率

14.60%

发文量

586

审稿时长

6.9 months

期刊介绍： The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.