{"title":"Distance to the nearest uncontrollable pair and algebraic Riccati equation","authors":"P. Gahinet","doi":"10.1109/CDC.1990.203595","DOIUrl":null,"url":null,"abstract":"A connection is established between nearness to unstabilizability of a stabilizable pair (A, B) of matrices, and nearness to singularity of the symmetric positive definite solution to an associated algebraic Riccati equation. From this result, computable upper and lower bounds are derived for the distance of (A, B) to the nearest uncontrollable pair.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"34 2","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"29th IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1990.203595","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
A connection is established between nearness to unstabilizability of a stabilizable pair (A, B) of matrices, and nearness to singularity of the symmetric positive definite solution to an associated algebraic Riccati equation. From this result, computable upper and lower bounds are derived for the distance of (A, B) to the nearest uncontrollable pair.<>
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