{"title":"离散时间饱和系统凸集不变性的充分必要条件","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":"{\"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}","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}
Necessary and sufficient conditions for invariance of convex sets for discrete-time saturated systems
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
