{"title":"Uniform stabilization of a Schrödinger equation with partial Dirichlet delayed control","authors":"Xiaorui Wang, Yanfang Li","doi":"10.1093/imamci/dnad022","DOIUrl":null,"url":null,"abstract":"\n In this paper, the uniform stabilization of a multi-dimensional Schrödinger equation with partial Dirichlet delayed control is concerned. The control input is suffered from time delay. Herein a new feedback controller is adopted in the investigation. Firstly, we rewrite the delayed system under consideration into a cascaded system of a transport equation and a Schrödinger equation, and construct an exponentially stable target system. Then by defining a bounded invertible linear transformation and choosing some appropriate kernel functions, we establish the equivalence between the closed-loop system and the target system. Finally, the exponential stability of the closed-loop system is obtained.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Mathematical Control and Information","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1093/imamci/dnad022","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the uniform stabilization of a multi-dimensional Schrödinger equation with partial Dirichlet delayed control is concerned. The control input is suffered from time delay. Herein a new feedback controller is adopted in the investigation. Firstly, we rewrite the delayed system under consideration into a cascaded system of a transport equation and a Schrödinger equation, and construct an exponentially stable target system. Then by defining a bounded invertible linear transformation and choosing some appropriate kernel functions, we establish the equivalence between the closed-loop system and the target system. Finally, the exponential stability of the closed-loop system is obtained.
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