{"title":"Exponentially stabilizing finite-dimensional controllers for linear distributed parameter systems","authors":"M. Balas","doi":"10.1109/CDC.1984.272298","DOIUrl":null,"url":null,"abstract":"The Galerkin method is presented as a way to develop finite-dimensional controllers for linear distributed parameter systems (DPS). The direct approach approximates the open-loop DPS and then generates the controller from this approximation; the indirect approach approximates the infinite-dimensional stabilizing controller. The indirect approach is shown to converge to the stable closed-loop system consisting of DPS and infinite-dimensional controller; conditions are presented on the behavior of the Galerkin method for the open loop DPS which guarantee closed-loop stability for large enough finite-dimensional approximations.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"127 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The 23rd IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1984.272298","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
The Galerkin method is presented as a way to develop finite-dimensional controllers for linear distributed parameter systems (DPS). The direct approach approximates the open-loop DPS and then generates the controller from this approximation; the indirect approach approximates the infinite-dimensional stabilizing controller. The indirect approach is shown to converge to the stable closed-loop system consisting of DPS and infinite-dimensional controller; conditions are presented on the behavior of the Galerkin method for the open loop DPS which guarantee closed-loop stability for large enough finite-dimensional approximations.
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