{"title":"Necessary and sufficient conditions for invariance of convex sets for discrete-time saturated systems","authors":"M. Fiacchini, C. Prieur, S. Tarbouriech","doi":"10.1109/CDC.2013.6760467","DOIUrl":null,"url":null,"abstract":"A convex analysis-based characterization of invariance and contractivity of compact convex sets for discretetime saturated systems is presented. Necessary and sufficient conditions for the existence of convex set-induced Lyapunov functions is provided. The results generalize the quadratic Lyapunov theory for saturated systems, apply also to asymmetric saturations and can be extended to affine nonlinearity maps. A numerical example illustrates the improvements of our method with respect to other classical ones.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"15 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"52nd IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2013.6760467","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
A convex analysis-based characterization of invariance and contractivity of compact convex sets for discretetime saturated systems is presented. Necessary and sufficient conditions for the existence of convex set-induced Lyapunov functions is provided. The results generalize the quadratic Lyapunov theory for saturated systems, apply also to asymmetric saturations and can be extended to affine nonlinearity maps. A numerical example illustrates the improvements of our method with respect to other classical ones.
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