{"title":"一个可稳定的切换线性系统不一定存在光滑齐次李雅普诺夫函数","authors":"F. Blanchini, P. Colaneri, M. E. Valcher","doi":"10.1109/CDC.2013.6760831","DOIUrl":null,"url":null,"abstract":"The contribution of this paper is twofold. Firstly, an example of a (positive) linear switched system that can be stabilized, via a controlled switching signal, but does not admit a smooth and positively homogeneous control Lyapunov function, is provided. The spectral properties of the subsystem matrices and of the Lyapunov candidates of the convex differential inclusion associated with the switched system, are thoroughly investigated. Secondly, by taking inspiration from the example, new feedback stabilization techniques for stabilizable positive switched systems are provided.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"97 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A stabilizable switched linear system does not necessarily admit a smooth homogeneous Lyapunov function\",\"authors\":\"F. Blanchini, P. Colaneri, M. E. Valcher\",\"doi\":\"10.1109/CDC.2013.6760831\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The contribution of this paper is twofold. Firstly, an example of a (positive) linear switched system that can be stabilized, via a controlled switching signal, but does not admit a smooth and positively homogeneous control Lyapunov function, is provided. The spectral properties of the subsystem matrices and of the Lyapunov candidates of the convex differential inclusion associated with the switched system, are thoroughly investigated. Secondly, by taking inspiration from the example, new feedback stabilization techniques for stabilizable positive switched systems are provided.\",\"PeriodicalId\":415568,\"journal\":{\"name\":\"52nd IEEE Conference on Decision and Control\",\"volume\":\"97 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"52nd IEEE Conference on Decision and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.2013.6760831\",\"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.2013.6760831","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A stabilizable switched linear system does not necessarily admit a smooth homogeneous Lyapunov function
The contribution of this paper is twofold. Firstly, an example of a (positive) linear switched system that can be stabilized, via a controlled switching signal, but does not admit a smooth and positively homogeneous control Lyapunov function, is provided. The spectral properties of the subsystem matrices and of the Lyapunov candidates of the convex differential inclusion associated with the switched system, are thoroughly investigated. Secondly, by taking inspiration from the example, new feedback stabilization techniques for stabilizable positive switched systems are provided.
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