{"title":"Stabilizability, I/O stability and coprime factorizations","authors":"Eduardo Sontag","doi":"10.1109/CDC.1988.194352","DOIUrl":null,"url":null,"abstract":"Coprime right factorizations are shown to exist for the input to state mapping of a continuous-time nonlinear system, provided that the smooth feedback stabilization problem be solvable for this system. As a particular case, it follows that feedback linearizable systems admit such factorizations. In order to establish this result, a Lyapunov-theoretic definition is proposed for bounded-input-bounded-output stability. The notion of stabilizability as studied in the state space nonlinear control literature is related to a notion of stability under bounded control perturbations analogous to those studied in operator-theoretic approaches to systems.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 27th IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1988.194352","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
Abstract
Coprime right factorizations are shown to exist for the input to state mapping of a continuous-time nonlinear system, provided that the smooth feedback stabilization problem be solvable for this system. As a particular case, it follows that feedback linearizable systems admit such factorizations. In order to establish this result, a Lyapunov-theoretic definition is proposed for bounded-input-bounded-output stability. The notion of stabilizability as studied in the state space nonlinear control literature is related to a notion of stability under bounded control perturbations analogous to those studied in operator-theoretic approaches to systems.<>
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