{"title":"有界传递函数线性系统补偿器的参数化","authors":"Yujiro Inouye","doi":"10.1109/CDC.1988.194700","DOIUrl":null,"url":null,"abstract":"A study is made of the feedback stabilization of a plant using a compensator, when the plant and the compensator belong to the class of linear discrete-time systems with matrix-valued transfer functions each entry of which is represented as a quotient of two analytic functions in the Hardy space H/sub infinity /. Such transfer functions are called functions of bounded type. A strong notion of right or left coprimeness is provided for the representations of these systems. It is shown that a linear system with a transfer function of bounded type always has a right-coprime representation and a left-coprime representation. Necessary and sufficient conditions are presented for such a plant to be stabilizable by a compensator. It is shown that under the stabilizability condition, it is possible to parameterize the set of all compensators that stabilize the plant.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":"{\"title\":\"Parametrization of compensators for linear systems with transfer functions of bounded type\",\"authors\":\"Yujiro Inouye\",\"doi\":\"10.1109/CDC.1988.194700\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A study is made of the feedback stabilization of a plant using a compensator, when the plant and the compensator belong to the class of linear discrete-time systems with matrix-valued transfer functions each entry of which is represented as a quotient of two analytic functions in the Hardy space H/sub infinity /. Such transfer functions are called functions of bounded type. A strong notion of right or left coprimeness is provided for the representations of these systems. It is shown that a linear system with a transfer function of bounded type always has a right-coprime representation and a left-coprime representation. Necessary and sufficient conditions are presented for such a plant to be stabilizable by a compensator. It is shown that under the stabilizability condition, it is possible to parameterize the set of all compensators that stabilize the plant.<<ETX>>\",\"PeriodicalId\":113534,\"journal\":{\"name\":\"Proceedings of the 27th IEEE Conference on Decision and Control\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"23\",\"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.1988.194700\",\"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.1988.194700","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Parametrization of compensators for linear systems with transfer functions of bounded type
A study is made of the feedback stabilization of a plant using a compensator, when the plant and the compensator belong to the class of linear discrete-time systems with matrix-valued transfer functions each entry of which is represented as a quotient of two analytic functions in the Hardy space H/sub infinity /. Such transfer functions are called functions of bounded type. A strong notion of right or left coprimeness is provided for the representations of these systems. It is shown that a linear system with a transfer function of bounded type always has a right-coprime representation and a left-coprime representation. Necessary and sufficient conditions are presented for such a plant to be stabilizable by a compensator. It is shown that under the stabilizability condition, it is possible to parameterize the set of all compensators that stabilize the plant.<>
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