{"title":"Wellposedness and stabilization of a class of infinite dimensional bilinear control systems","authors":"J. Daafouz, M. Tucsnak, J. Valein","doi":"10.1109/CDC.2012.6426706","DOIUrl":null,"url":null,"abstract":"We consider a class of infinite dimensional systems involving a control function u taking values in [0; 1]. This class contains, in particular, the average models of some infinite dimensional switched systems. We prove that the system is well-posed and obtain some regularity properties. Moreover, when u is given in an appropriate feedback form and the system satisfies appropriate observability assumptions, we show that the system is weakly stable. The main example concerns the analysis and stabilization of a model of Boost converter connected to a load via a transmission line. The main novelty consists in the fact that we give a rigorous wellposedness and stability analysis of coupled systems, in the presence of duty cycles.","PeriodicalId":312426,"journal":{"name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2012.6426706","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We consider a class of infinite dimensional systems involving a control function u taking values in [0; 1]. This class contains, in particular, the average models of some infinite dimensional switched systems. We prove that the system is well-posed and obtain some regularity properties. Moreover, when u is given in an appropriate feedback form and the system satisfies appropriate observability assumptions, we show that the system is weakly stable. The main example concerns the analysis and stabilization of a model of Boost converter connected to a load via a transmission line. The main novelty consists in the fact that we give a rigorous wellposedness and stability analysis of coupled systems, in the presence of duty cycles.