{"title":"Stability and angles between state matrices of positive linear systems","authors":"T. Kaczorek","doi":"10.1109/MMAR.2019.8864610","DOIUrl":null,"url":null,"abstract":"The stability and the angles between state matrices of positive continuous-time and discrete-time linear systems are addressed. It is shown that: 1) The angles between matrices can be useful tool for analysis of the stability of positive continuous-time and discrete-time linear systems; 2) The positive linear system is asymptotically stable if and only if the symmetrical part of the state matrix is Hurwitz for continuous-time systems and Schur for discrete-time systems; 3) Using the angles between matrices necessary and sufficient conditions are established for the asymptotic stability of the positive linear systemst.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MMAR.2019.8864610","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The stability and the angles between state matrices of positive continuous-time and discrete-time linear systems are addressed. It is shown that: 1) The angles between matrices can be useful tool for analysis of the stability of positive continuous-time and discrete-time linear systems; 2) The positive linear system is asymptotically stable if and only if the symmetrical part of the state matrix is Hurwitz for continuous-time systems and Schur for discrete-time systems; 3) Using the angles between matrices necessary and sufficient conditions are established for the asymptotic stability of the positive linear systemst.
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