{"title":"改进的循环函数法，用于分析与停留时间有关的脉冲系统稳定性","authors":"Hong-Bing Zeng, Wei-Min Wang, Wei Wang, Hui-Qin Xiao","doi":"10.1016/j.nahs.2024.101477","DOIUrl":null,"url":null,"abstract":"<div><p>This paper studies the dwell-time-dependent stability analysis of impulsive systems by using a new time-square-dependent looped-functional. Based on the Lyapunov theory and two-sided looped-functional method, a time-square-dependent looped-functional is proposed, which fully utilizes the information of both the intervals <span><math><mrow><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>,</mo><mi>t</mi><mo>]</mo></mrow></math></span> and <span><math><mrow><mo>[</mo><mi>t</mi><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>]</mo></mrow></math></span>. Then, by applying Jensen’s inequality and free-matrix-based inequalities to deal with integral terms in the functional derivatives, sufficient stability conditions in the form of linear matrix inequality are derived for periodic and aperiodic impulsive systems. Finally, numerical examples and simulation tests are given to illustrate the effectiveness and superiority of the proposed method.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"52 ","pages":"Article 101477"},"PeriodicalIF":3.7000,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Improved looped-functional approach for dwell-time-dependent stability analysis of impulsive systems\",\"authors\":\"Hong-Bing Zeng, Wei-Min Wang, Wei Wang, Hui-Qin Xiao\",\"doi\":\"10.1016/j.nahs.2024.101477\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper studies the dwell-time-dependent stability analysis of impulsive systems by using a new time-square-dependent looped-functional. Based on the Lyapunov theory and two-sided looped-functional method, a time-square-dependent looped-functional is proposed, which fully utilizes the information of both the intervals <span><math><mrow><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>,</mo><mi>t</mi><mo>]</mo></mrow></math></span> and <span><math><mrow><mo>[</mo><mi>t</mi><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>]</mo></mrow></math></span>. Then, by applying Jensen’s inequality and free-matrix-based inequalities to deal with integral terms in the functional derivatives, sufficient stability conditions in the form of linear matrix inequality are derived for periodic and aperiodic impulsive systems. Finally, numerical examples and simulation tests are given to illustrate the effectiveness and superiority of the proposed method.</p></div>\",\"PeriodicalId\":49011,\"journal\":{\"name\":\"Nonlinear Analysis-Hybrid Systems\",\"volume\":\"52 \",\"pages\":\"Article 101477\"},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-02-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Hybrid Systems\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1751570X24000141\",\"RegionNum\":2,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Hybrid Systems","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1751570X24000141","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Improved looped-functional approach for dwell-time-dependent stability analysis of impulsive systems
This paper studies the dwell-time-dependent stability analysis of impulsive systems by using a new time-square-dependent looped-functional. Based on the Lyapunov theory and two-sided looped-functional method, a time-square-dependent looped-functional is proposed, which fully utilizes the information of both the intervals and . Then, by applying Jensen’s inequality and free-matrix-based inequalities to deal with integral terms in the functional derivatives, sufficient stability conditions in the form of linear matrix inequality are derived for periodic and aperiodic impulsive systems. Finally, numerical examples and simulation tests are given to illustrate the effectiveness and superiority of the proposed method.
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Nonlinear Analysis: Hybrid Systems welcomes all important research and expository papers in any discipline. Papers that are principally concerned with the theory of hybrid systems should contain significant results indicating relevant applications. Papers that emphasize applications should consist of important real world models and illuminating techniques. Papers that interrelate various aspects of hybrid systems will be most welcome.
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