{"title":"NEW CRITERION OF STABILITY FOR TIME-VARYING DYNAMICAL SYSTEMS: APPLICATION TO SPRING-MASS-DAMPER MODEL","authors":"Ezzine Faten, Mohamed Ali Hammami","doi":"10.1016/S0034-4877(23)00007-1","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate the problem of stability with respect to a part of variables of nonlinear time-varying systems. We derive some sufficient conditions that guarantee exponential stability and practical exponential stability with respect to a part of the variables of perturbed systems based on Lyapunov techniques where converse theorems are stated. Furthermore, illustrative examples to show the usefulness and applicability of the theory of stability with respect to a part of variables are provided. In particular, we show that our approach can be applied to the spring-mass-damper model.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"91 1","pages":"Pages 1-28"},"PeriodicalIF":1.0000,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487723000071","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate the problem of stability with respect to a part of variables of nonlinear time-varying systems. We derive some sufficient conditions that guarantee exponential stability and practical exponential stability with respect to a part of the variables of perturbed systems based on Lyapunov techniques where converse theorems are stated. Furthermore, illustrative examples to show the usefulness and applicability of the theory of stability with respect to a part of variables are provided. In particular, we show that our approach can be applied to the spring-mass-damper model.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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