Stabilization of nonhomogenous semi-Markov jump linear systems with synchronous switching delays via aperiodically intermittent control

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-21 DOI:10.1016/j.cnsns.2024.108357

{"title":"Stabilization of nonhomogenous semi-Markov jump linear systems with synchronous switching delays via aperiodically intermittent control","authors":"","doi":"10.1016/j.cnsns.2024.108357","DOIUrl":null,"url":null,"abstract":"<div><div>A type of nonhomogenous semi-Markov jump linear systems with synchronous switching delays is considered in the present paper. Owing to the existence of time-varying delays and nonhomogenous semi-Markov switching process, the selection of Lyapunov functional and the transformation of some time-varying parameters become more complicated in comparison with many existing works. To overcome these difficulties, a sort of Lyapunov–Krasovskii functional related to switching delays is introduced. Simultaneously, the technique of convex combination is applied to tackle a variety of time-varying terms including transition probabilities (TPs), probability distribution function and probability density function (PDF). Then, a time-invariant stability criterion superior to many relevant works in conservativeness is obtained to ensure mean-square exponential stability (MES). Based on this result, time-invariant conditions for mean square exponential stability of the controlled system are also attained by the continuous feedback control. Subsequently, to stand on the point of cost reduction, an aperiodically intermittent control (AIC) is adopted in such a system and a stability criterion is attained as well under more relaxed restrictions on relative parameters. Finally, a numerical example is provided to verify the effectiveness and correctness of the results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424005422","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

A type of nonhomogenous semi-Markov jump linear systems with synchronous switching delays is considered in the present paper. Owing to the existence of time-varying delays and nonhomogenous semi-Markov switching process, the selection of Lyapunov functional and the transformation of some time-varying parameters become more complicated in comparison with many existing works. To overcome these difficulties, a sort of Lyapunov–Krasovskii functional related to switching delays is introduced. Simultaneously, the technique of convex combination is applied to tackle a variety of time-varying terms including transition probabilities (TPs), probability distribution function and probability density function (PDF). Then, a time-invariant stability criterion superior to many relevant works in conservativeness is obtained to ensure mean-square exponential stability (MES). Based on this result, time-invariant conditions for mean square exponential stability of the controlled system are also attained by the continuous feedback control. Subsequently, to stand on the point of cost reduction, an aperiodically intermittent control (AIC) is adopted in such a system and a stability criterion is attained as well under more relaxed restrictions on relative parameters. Finally, a numerical example is provided to verify the effectiveness and correctness of the results.

查看原文本刊更多论文

通过周期性间歇控制稳定具有同步开关延迟的非同源半马尔可夫跃迁线性系统

本文研究了一种具有同步切换延迟的非同质半马尔可夫跃迁线性系统。由于时变延迟和非均质半马尔科夫切换过程的存在，与许多现有研究相比，李亚普诺夫函数的选择和一些时变参数的变换变得更加复杂。为了克服这些困难，我们引入了一种与切换延迟相关的 Lyapunov-Krasovskii 函数。同时，应用凸组合技术来处理各种时变项，包括过渡概率（TPs）、概率分布函数和概率密度函数（PDF）。然后，得到了一个在保守性方面优于许多相关研究的时变稳定性准则，以确保均方指数稳定性（MES）。在此基础上，通过连续反馈控制，还获得了被控系统均方指数稳定性的时变条件。随后，从降低成本的角度出发，在这种系统中采用了周期性间歇控制（AIC），并在相对参数限制更宽松的情况下也达到了稳定标准。最后，提供了一个数值示例来验证结果的有效性和正确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.