{"title":"三维齐次反馈律","authors":"M. Kawski","doi":"10.1109/CDC.1989.70364","DOIUrl":null,"url":null,"abstract":"Consideration is given to single-input systems on R/sup 3/ that are small-time locally controllable. The inherent symmetries of the standard nilpotent approximations to such systems are used to show how to construct Holder continuous feedback laws that respect the symmetries and asymptotically stabilize the control system. An explicit example is worked in detail, and a necessary condition for the existence of such stabilizing feedback laws is obtained.<<ETX>>","PeriodicalId":156565,"journal":{"name":"Proceedings of the 28th IEEE Conference on Decision and Control,","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1989-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"Homogeneous feedback laws in dimension three\",\"authors\":\"M. Kawski\",\"doi\":\"10.1109/CDC.1989.70364\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consideration is given to single-input systems on R/sup 3/ that are small-time locally controllable. The inherent symmetries of the standard nilpotent approximations to such systems are used to show how to construct Holder continuous feedback laws that respect the symmetries and asymptotically stabilize the control system. An explicit example is worked in detail, and a necessary condition for the existence of such stabilizing feedback laws is obtained.<<ETX>>\",\"PeriodicalId\":156565,\"journal\":{\"name\":\"Proceedings of the 28th IEEE Conference on Decision and Control,\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 28th IEEE Conference on Decision and Control,\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1989.70364\",\"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 28th IEEE Conference on Decision and Control,","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1989.70364","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Consideration is given to single-input systems on R/sup 3/ that are small-time locally controllable. The inherent symmetries of the standard nilpotent approximations to such systems are used to show how to construct Holder continuous feedback laws that respect the symmetries and asymptotically stabilize the control system. An explicit example is worked in detail, and a necessary condition for the existence of such stabilizing feedback laws is obtained.<>
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