{"title":"稳定性，I/O稳定性和质因数分解","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":"{\"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}","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}
Stabilizability, I/O stability and coprime factorizations
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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