{"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}
引用次数: 4
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-¿
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
