{"title":"Estimating the robust domain of attraction for difference inclusions using an interval Lyapunov equation","authors":"","doi":"10.1016/j.sysconle.2024.105911","DOIUrl":null,"url":null,"abstract":"<div><p>We present a method for estimating the domain of attraction of a discrete-time system with uncertainty. Difference inclusions are used to model the system’s dynamics. Two conditions (invariance and negative definiteness) are derived in terms of the Lyapunov stability of the systems. We propose an interval version of the Lyapunov equation, which ensures the negative definiteness for a given Lyapunov function. Then, we introduce some sufficient conditions for invariance. Finally, the estimation of the domain of attraction is extended by solving an optimization problem. These results do not assume that the Lyapunov function is quadratic and can be fully applied even in the presence of control input saturation and uncertainty, such as aperiodic sampled-data. Some numerical examples validate the method and compare it with other approaches presented in this work.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691124001993","RegionNum":3,"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
Abstract
We present a method for estimating the domain of attraction of a discrete-time system with uncertainty. Difference inclusions are used to model the system’s dynamics. Two conditions (invariance and negative definiteness) are derived in terms of the Lyapunov stability of the systems. We propose an interval version of the Lyapunov equation, which ensures the negative definiteness for a given Lyapunov function. Then, we introduce some sufficient conditions for invariance. Finally, the estimation of the domain of attraction is extended by solving an optimization problem. These results do not assume that the Lyapunov function is quadratic and can be fully applied even in the presence of control input saturation and uncertainty, such as aperiodic sampled-data. Some numerical examples validate the method and compare it with other approaches presented in this work.
期刊介绍：
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.
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