Exponential stability of fractional order impulsive switched system with stable and unstable subsystems

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-05-22 DOI:10.1016/j.cnsns.2025.108940

Qinqin Liao, Danfeng Luo

{"title":"Exponential stability of fractional order impulsive switched system with stable and unstable subsystems","authors":"Qinqin Liao, Danfeng Luo","doi":"10.1016/j.cnsns.2025.108940","DOIUrl":null,"url":null,"abstract":"<div><div>The exponential stability of the Caputo fractional order impulsive switched system (CFOISS) consisting of stable and unstable subsystems is addressed in this paper. We integrate the multiple Lyapunov function (MLFs) approach, the mode-dependent average dwell time (MDADT) method, and the fast-slow switching concept to handle the switched sequence. In order to better represent the impulse, we further employ the mode-dependent average impulsive interval (MDAII) technique to process the impulsive sequence. The relationship between impulsive intensity, system mode, MDADT and MDAII is successfully established by considering the synchronization and complete asynchronism of impulse and switched time, respectively, and a set of low conservative sufficient conditions is derived. The results show that CFOISS can achieve exponential stability under certain switching rule when the state trajectory can be compensated by the slow switching stable subsystem for the impact of the quick switching unstable subsystem, and the jump of the impulsive point is within a certain range. Finally, the stability of the proposed method is verified by several numerical simulation examples.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108940"},"PeriodicalIF":3.4000,"publicationDate":"2025-05-22","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/S100757042500351X","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

The exponential stability of the Caputo fractional order impulsive switched system (CFOISS) consisting of stable and unstable subsystems is addressed in this paper. We integrate the multiple Lyapunov function (MLFs) approach, the mode-dependent average dwell time (MDADT) method, and the fast-slow switching concept to handle the switched sequence. In order to better represent the impulse, we further employ the mode-dependent average impulsive interval (MDAII) technique to process the impulsive sequence. The relationship between impulsive intensity, system mode, MDADT and MDAII is successfully established by considering the synchronization and complete asynchronism of impulse and switched time, respectively, and a set of low conservative sufficient conditions is derived. The results show that CFOISS can achieve exponential stability under certain switching rule when the state trajectory can be compensated by the slow switching stable subsystem for the impact of the quick switching unstable subsystem, and the jump of the impulsive point is within a certain range. Finally, the stability of the proposed method is verified by several numerical simulation examples.

查看原文本刊更多论文

具有稳定和不稳定子系统的分数阶脉冲切换系统的指数稳定性

研究了由稳定子系统和不稳定子系统组成的Caputo分数阶脉冲切换系统（CFOISS）的指数稳定性。我们将多重Lyapunov函数（mlf）方法、模式相关平均停留时间（MDADT）方法和快慢切换概念集成在一起来处理切换序列。为了更好地表示脉冲，我们进一步采用模式相关平均脉冲间隔（mdai）技术对脉冲序列进行处理。分别考虑脉冲和切换时间的同步性和完全异步性，成功地建立了脉冲强度、系统模式、MDADT和mdai之间的关系，并导出了一组低保守性的充分条件。结果表明，当状态轨迹可以由慢速切换稳定子系统补偿快速切换不稳定子系统的影响，且脉冲点的跳变在一定范围内时，CFOISS可以在一定的切换规则下实现指数稳定。最后，通过数值仿真算例验证了所提方法的稳定性。

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.