具有确定性和随机切换信号的Caputo分数阶切换线性系统的几乎肯定稳定性

IF 1.7 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Automatika Pub Date : 2023-10-02 DOI:10.1080/00051144.2023.2262016

Qixiang Wang, Fei Long, Lipo Mo, Jing Yang

{"title":"具有确定性和随机切换信号的Caputo分数阶切换线性系统的几乎肯定稳定性","authors":"Qixiang Wang, Fei Long, Lipo Mo, Jing Yang","doi":"10.1080/00051144.2023.2262016","DOIUrl":null,"url":null,"abstract":"In this paper, we address the almost sure stability problem of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals (DS-CFLSs). Firstly, due to the non-locality and memory of fractional-order switched systems, an inequality is proposed to solve the difficulties in the discussion of stability. Then, for DS-CFLSs, a deterministic switching strategy is predesigned, and stochastic switching signals are generated by the Markov process. After that, for the globally asymptotic stability almost surely (GAS a.s.) and exponential stability almost surely (ES a.s.) of DS-CFLSs, some sufficient conditions are proposed by using the multi-Lyapunov function and probability analysis methods. Finally, some numerical examples show that our results are effective.","PeriodicalId":55412,"journal":{"name":"Automatika","volume":"49 1","pages":"0"},"PeriodicalIF":1.7000,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Almost sure stability of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals\",\"authors\":\"Qixiang Wang, Fei Long, Lipo Mo, Jing Yang\",\"doi\":\"10.1080/00051144.2023.2262016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we address the almost sure stability problem of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals (DS-CFLSs). Firstly, due to the non-locality and memory of fractional-order switched systems, an inequality is proposed to solve the difficulties in the discussion of stability. Then, for DS-CFLSs, a deterministic switching strategy is predesigned, and stochastic switching signals are generated by the Markov process. After that, for the globally asymptotic stability almost surely (GAS a.s.) and exponential stability almost surely (ES a.s.) of DS-CFLSs, some sufficient conditions are proposed by using the multi-Lyapunov function and probability analysis methods. Finally, some numerical examples show that our results are effective.\",\"PeriodicalId\":55412,\"journal\":{\"name\":\"Automatika\",\"volume\":\"49 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-10-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Automatika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/00051144.2023.2262016\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00051144.2023.2262016","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了具有确定性和随机开关信号的Caputo分数阶开关线性系统的几乎确定稳定性问题。首先，针对分数阶切换系统的非局域性和记忆性，提出了一个不等式来解决稳定性问题。然后，针对ds - cfls，预先设计了确定性开关策略，利用马尔可夫过程生成随机开关信号。在此基础上，利用多重lyapunov函数和概率分析方法，给出了ds - cfls的全局渐近几乎肯定稳定(GAS as)和指数几乎肯定稳定(ES as)的充分条件。最后，通过数值算例验证了所得结果的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Almost sure stability of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals

In this paper, we address the almost sure stability problem of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals (DS-CFLSs). Firstly, due to the non-locality and memory of fractional-order switched systems, an inequality is proposed to solve the difficulties in the discussion of stability. Then, for DS-CFLSs, a deterministic switching strategy is predesigned, and stochastic switching signals are generated by the Markov process. After that, for the globally asymptotic stability almost surely (GAS a.s.) and exponential stability almost surely (ES a.s.) of DS-CFLSs, some sufficient conditions are proposed by using the multi-Lyapunov function and probability analysis methods. Finally, some numerical examples show that our results are effective.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Automatika AUTOMATION & CONTROL SYSTEMS-ENGINEERING, ELECTRICAL & ELECTRONIC

CiteScore

4.00

自引率

5.30%

发文量

审稿时长

4.5 months

期刊介绍： AUTOMATIKA – Journal for Control, Measurement, Electronics, Computing and Communications is an international scientific journal that publishes scientific and professional papers in the field of automatic control, robotics, measurements, electronics, computing, communications and related areas. Click here for full Focus & Scope. AUTOMATIKA is published since 1960, and since 1991 by KoREMA - Croatian Society for Communications, Computing, Electronics, Measurement and Control, Member of IMEKO and IFAC.