{"title":"用lyapunov - krasovskii和razumikhin方法的结合研究时滞系统的渐近平衡","authors":"S. Kuptsova, S. Y. Kuptsov","doi":"10.21638/11701/spbu10.2022.201","DOIUrl":null,"url":null,"abstract":"The nonlinear time-delay systems are considered and the limiting Behavior of their solutions is investigated. The case in which the solutions have a trivial equilibrium that may not be an invariant set of the system is studied. The junction of Lyapunov - Krasovskii and Razumikhin approaches is applied to obtain sufficient conditions for the existence of an asymptotic quiescent position in the large. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are obtained. Examples, that illustrate the application of the obtained results, are given.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"RESEARCH OF THE ASYMPTOTIC EQUILIBRIUM OF TIME-DELAY SYSTEMS BY JUNCTION OF LYAPUNOV - KRASOVSKII AND RAZUMIKHIN APPROACHES\",\"authors\":\"S. Kuptsova, S. Y. Kuptsov\",\"doi\":\"10.21638/11701/spbu10.2022.201\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The nonlinear time-delay systems are considered and the limiting Behavior of their solutions is investigated. The case in which the solutions have a trivial equilibrium that may not be an invariant set of the system is studied. The junction of Lyapunov - Krasovskii and Razumikhin approaches is applied to obtain sufficient conditions for the existence of an asymptotic quiescent position in the large. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are obtained. Examples, that illustrate the application of the obtained results, are given.\",\"PeriodicalId\":43738,\"journal\":{\"name\":\"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21638/11701/spbu10.2022.201\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21638/11701/spbu10.2022.201","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
RESEARCH OF THE ASYMPTOTIC EQUILIBRIUM OF TIME-DELAY SYSTEMS BY JUNCTION OF LYAPUNOV - KRASOVSKII AND RAZUMIKHIN APPROACHES
The nonlinear time-delay systems are considered and the limiting Behavior of their solutions is investigated. The case in which the solutions have a trivial equilibrium that may not be an invariant set of the system is studied. The junction of Lyapunov - Krasovskii and Razumikhin approaches is applied to obtain sufficient conditions for the existence of an asymptotic quiescent position in the large. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are obtained. Examples, that illustrate the application of the obtained results, are given.
期刊介绍：
The journal is the prime outlet for the findings of scientists from the Faculty of applied mathematics and control processes of St. Petersburg State University. It publishes original contributions in all areas of applied mathematics, computer science and control. Vestnik St. Petersburg University: Applied Mathematics. Computer Science. Control Processes features articles that cover the major areas of applied mathematics, computer science and control.
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