{"title":"The stability of differential-difference systems with linearly increasing delay. II. Systems with additive right side","authors":"A. Ekimov, A. P. Zhabko, P. Yakovlev","doi":"10.21638/11701/spbu10.2023.101","DOIUrl":null,"url":null,"abstract":"The article considers an uncontrolled system of differential-difference equations with a homogeneous additive right side and linearly increasing delay. Sufficient conditions for asymptotic stability are known for a number of special cases of such systems. Razumikhin's theorem on the asymptotic stability of homogeneous systems with proportional delay is formulated. Sufficient conditions for asymptotic stability are obtained basing on the asymptotic stability of the initial system without delay and constructing the Lyapunov function.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"21 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2023-01-01","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/spbu10.2023.101","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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Abstract
The article considers an uncontrolled system of differential-difference equations with a homogeneous additive right side and linearly increasing delay. Sufficient conditions for asymptotic stability are known for a number of special cases of such systems. Razumikhin's theorem on the asymptotic stability of homogeneous systems with proportional delay is formulated. Sufficient conditions for asymptotic stability are obtained basing on the asymptotic stability of the initial system without delay and constructing the Lyapunov function.
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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