{"title":"Construction of Diagonal Lyapunov–Krasovskii Functionals for a Class of Positive Differential-Algebraic Systems","authors":"A. Yu. Aleksandrov","doi":"10.1134/s001226612405001x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A coupled system describing the interaction of a differential subsystem with nonlinearities\nof a sector type and a linear difference subsystem is considered. It is assumed that the system is\npositive. A diagonal Lyapunov–Krasovskii functional is constructed, and conditions are\ndetermined under which the absolute stability of the system can be proved with the use of such a\nfunctional. In the case of power-law nonlinearities, estimates for the rate of convergence of the\nsolution to the origin are obtained. The stability of the corresponding system with parameter\nswitching is analyzed. Sufficient conditions guaranteeing the asymptotic stability of the zero\nsolution for any admissible switching law are obtained.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s001226612405001x","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
A coupled system describing the interaction of a differential subsystem with nonlinearities
of a sector type and a linear difference subsystem is considered. It is assumed that the system is
positive. A diagonal Lyapunov–Krasovskii functional is constructed, and conditions are
determined under which the absolute stability of the system can be proved with the use of such a
functional. In the case of power-law nonlinearities, estimates for the rate of convergence of the
solution to the origin are obtained. The stability of the corresponding system with parameter
switching is analyzed. Sufficient conditions guaranteeing the asymptotic stability of the zero
solution for any admissible switching law are obtained.
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