{"title":"参数相关李雅普诺夫函数反例的数值验证","authors":"Birgül Aksoy, Taner Büyükköroğlu, Vakif Dzhafarov","doi":"10.1016/j.amc.2024.129246","DOIUrl":null,"url":null,"abstract":"<div><div>We consider the existence problem of an affine parameter-dependent quadratic Lyapunov function for a robust Hurwitz stable matrix segment. Numerical verification of the known counterexample to the known Barmish's conjecture is provided. Second order parameter-dependent quadratic Lyapunov function for this counterexample is constructed. Sufficient conditions for the existence of an affine parameter-dependent Lyapunov function are given.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"492 ","pages":"Article 129246"},"PeriodicalIF":3.5000,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the numerical verification of a counterexample on parameter-dependent Lyapunov functions\",\"authors\":\"Birgül Aksoy, Taner Büyükköroğlu, Vakif Dzhafarov\",\"doi\":\"10.1016/j.amc.2024.129246\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We consider the existence problem of an affine parameter-dependent quadratic Lyapunov function for a robust Hurwitz stable matrix segment. Numerical verification of the known counterexample to the known Barmish's conjecture is provided. Second order parameter-dependent quadratic Lyapunov function for this counterexample is constructed. Sufficient conditions for the existence of an affine parameter-dependent Lyapunov function are given.</div></div>\",\"PeriodicalId\":55496,\"journal\":{\"name\":\"Applied Mathematics and Computation\",\"volume\":\"492 \",\"pages\":\"Article 129246\"},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2024-12-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0096300324007070\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324007070","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
On the numerical verification of a counterexample on parameter-dependent Lyapunov functions
We consider the existence problem of an affine parameter-dependent quadratic Lyapunov function for a robust Hurwitz stable matrix segment. Numerical verification of the known counterexample to the known Barmish's conjecture is provided. Second order parameter-dependent quadratic Lyapunov function for this counterexample is constructed. Sufficient conditions for the existence of an affine parameter-dependent Lyapunov function are given.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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