{"title":"可控系统的摄动","authors":"R. O'Brien","doi":"10.1109/CDC.1978.267937","DOIUrl":null,"url":null,"abstract":"Let a semi-dynamical system, (A,B): (A,B) x=Ax + Bu x(0) = 0 be given on a Hilbert space X. When A is self-adjoint and semi-bounded with spectral measure E(¿) it is shown that controllability of the system (A,B) is equivalent to that of (f(A), B) where f(¿) is any semi-bounded, Borel measurable E(¿)-surjective function on-¿<t<+¿. In particular (A,B) is controllable if and only if (A¿, B) is controllable A¿=-(-A)¿. These results are then extended to the case where A generates a unlformly bounded C0 - semigroup on X and are applied to a system whose dynamics are governed by the singular integral operator generating the Poisson integral semigroup.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"721 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1979-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Perturbation of controllable systems\",\"authors\":\"R. O'Brien\",\"doi\":\"10.1109/CDC.1978.267937\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let a semi-dynamical system, (A,B): (A,B) x=Ax + Bu x(0) = 0 be given on a Hilbert space X. When A is self-adjoint and semi-bounded with spectral measure E(¿) it is shown that controllability of the system (A,B) is equivalent to that of (f(A), B) where f(¿) is any semi-bounded, Borel measurable E(¿)-surjective function on-¿<t<+¿. In particular (A,B) is controllable if and only if (A¿, B) is controllable A¿=-(-A)¿. These results are then extended to the case where A generates a unlformly bounded C0 - semigroup on X and are applied to a system whose dynamics are governed by the singular integral operator generating the Poisson integral semigroup.\",\"PeriodicalId\":375119,\"journal\":{\"name\":\"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes\",\"volume\":\"721 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1979-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1978.267937\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1978.267937","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
摘要
在希尔伯特空间x上给出一个半动力系统(a,B):(a,B) x=Ax + Bu x(0) = 0，当a是自伴半有界且谱测度E(¿)时，证明了系统(a,B)的可控性等价于系统(f(a)， B)的可控性，其中f(¿)是在-¿本文章由计算机程序翻译，如有差异，请以英文原文为准。
Let a semi-dynamical system, (A,B): (A,B) x=Ax + Bu x(0) = 0 be given on a Hilbert space X. When A is self-adjoint and semi-bounded with spectral measure E(¿) it is shown that controllability of the system (A,B) is equivalent to that of (f(A), B) where f(¿) is any semi-bounded, Borel measurable E(¿)-surjective function on-¿
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