{"title":"微分夹杂的线性化","authors":"Mira Bivas, M. Krastanov, N. Ribarska","doi":"10.55630/serdica.2023.49.187-204","DOIUrl":null,"url":null,"abstract":"In this paper we extend the approach of Dubovickiĭ and Miljutin for linearization of the dynamics of smooth control systems to a non-smooth setting. We consider dynamics governed by a differential inclusion and we study the Clarke tangent cone to the set of all admissible trajectories starting from a fixed point. Our approach is based on the classical Filippov’s theorem and on the important property “subtransversality” of two closed sets.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"63 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linearization of differential inclusions\",\"authors\":\"Mira Bivas, M. Krastanov, N. Ribarska\",\"doi\":\"10.55630/serdica.2023.49.187-204\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we extend the approach of Dubovickiĭ and Miljutin for linearization of the dynamics of smooth control systems to a non-smooth setting. We consider dynamics governed by a differential inclusion and we study the Clarke tangent cone to the set of all admissible trajectories starting from a fixed point. Our approach is based on the classical Filippov’s theorem and on the important property “subtransversality” of two closed sets.\",\"PeriodicalId\":509503,\"journal\":{\"name\":\"Serdica Mathematical Journal\",\"volume\":\"63 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Serdica Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55630/serdica.2023.49.187-204\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Serdica Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55630/serdica.2023.49.187-204","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper we extend the approach of Dubovickiĭ and Miljutin for linearization of the dynamics of smooth control systems to a non-smooth setting. We consider dynamics governed by a differential inclusion and we study the Clarke tangent cone to the set of all admissible trajectories starting from a fixed point. Our approach is based on the classical Filippov’s theorem and on the important property “subtransversality” of two closed sets.
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