{"title":"An LMI approach to L/sub 2/ gain analysis and control synthesis of switched systems","authors":"D. Xie, Long Wang, G. Xie, Fei Hao","doi":"10.1109/CACSD.2004.1393901","DOIUrl":null,"url":null,"abstract":"This paper investigates the L/sub 2/ gain analysis and control synthesis of discrete-time switched systems under arbitrary switching by linear matrix inequality (LMI) approach together with switched Lyapunov function method. First, the existence of a switched Lyapunov function is proven to be equivalent to the feasibility of some LMIs. An upper bound of the L/sub 2/ gain for switched systems can be computed by solving an eigenvalue problem (EVP). Then, we design a switched state feedback controller and a switched output feedback controller, respectively, guaranteeing that the corresponding closed-loop system is asymptotically stable with an L/sub 2/ gain smaller than a fixed constant. LMI-based conditions for both cases are presented. Finally, two examples are given to illustrate our results.","PeriodicalId":111199,"journal":{"name":"2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CACSD.2004.1393901","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
This paper investigates the L/sub 2/ gain analysis and control synthesis of discrete-time switched systems under arbitrary switching by linear matrix inequality (LMI) approach together with switched Lyapunov function method. First, the existence of a switched Lyapunov function is proven to be equivalent to the feasibility of some LMIs. An upper bound of the L/sub 2/ gain for switched systems can be computed by solving an eigenvalue problem (EVP). Then, we design a switched state feedback controller and a switched output feedback controller, respectively, guaranteeing that the corresponding closed-loop system is asymptotically stable with an L/sub 2/ gain smaller than a fixed constant. LMI-based conditions for both cases are presented. Finally, two examples are given to illustrate our results.
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