{"title":"Metzler矩阵多面体的特征值右外界及其系统应用","authors":"O. Pastravanu, M. Matcovschi","doi":"10.1109/ISSCS.2017.8034897","DOIUrl":null,"url":null,"abstract":"Metzler matrices are algebraically characterized by having nonnegative off-diagonal entries and, from the dynamical point of view, define continuous-time positive systems. Our work studies polytopes of Metzler matrices and linear dynamics generated by such sets. The first part of the paper explores the algebraic properties of matrix polytopes, by focusing on the estimation of a right outer bound for all eigenvalues. The second part analyzes the dynamical properties of positive polytopic systems, by revealing connections between the estimated right outer bound and the evolution of trajectories (related to copositive Lyapunov functions and invariant sets).","PeriodicalId":338255,"journal":{"name":"2017 International Symposium on Signals, Circuits and Systems (ISSCS)","volume":"119 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Eigenvalue right-outer bounds for polytopes of Metzler matrices and systems applications\",\"authors\":\"O. Pastravanu, M. Matcovschi\",\"doi\":\"10.1109/ISSCS.2017.8034897\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Metzler matrices are algebraically characterized by having nonnegative off-diagonal entries and, from the dynamical point of view, define continuous-time positive systems. Our work studies polytopes of Metzler matrices and linear dynamics generated by such sets. The first part of the paper explores the algebraic properties of matrix polytopes, by focusing on the estimation of a right outer bound for all eigenvalues. The second part analyzes the dynamical properties of positive polytopic systems, by revealing connections between the estimated right outer bound and the evolution of trajectories (related to copositive Lyapunov functions and invariant sets).\",\"PeriodicalId\":338255,\"journal\":{\"name\":\"2017 International Symposium on Signals, Circuits and Systems (ISSCS)\",\"volume\":\"119 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2017 International Symposium on Signals, Circuits and Systems (ISSCS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISSCS.2017.8034897\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 International Symposium on Signals, Circuits and Systems (ISSCS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISSCS.2017.8034897","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Eigenvalue right-outer bounds for polytopes of Metzler matrices and systems applications
Metzler matrices are algebraically characterized by having nonnegative off-diagonal entries and, from the dynamical point of view, define continuous-time positive systems. Our work studies polytopes of Metzler matrices and linear dynamics generated by such sets. The first part of the paper explores the algebraic properties of matrix polytopes, by focusing on the estimation of a right outer bound for all eigenvalues. The second part analyzes the dynamical properties of positive polytopic systems, by revealing connections between the estimated right outer bound and the evolution of trajectories (related to copositive Lyapunov functions and invariant sets).
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