{"title":"线性时变观测系统的静止轨道","authors":"A. Astrovskii","doi":"10.29235/1561-8323-2021-65-1-18-24","DOIUrl":null,"url":null,"abstract":"In terms of matrix observability, the necessary and sufficient conditions are obtained for the linear timevarying observation system to have stationary orbits with respect to the linear time-varying transformation group of class C1 . The full invariant of the action of a transformation group is described. It is proved that for any matrix function A c C(T, Rn×n ), there exists such an n-vector function c(t), t c T, that the pair (A, c) is uniformly observable. The algorithm for constructing a stationary system is described.","PeriodicalId":11283,"journal":{"name":"Doklady of the National Academy of Sciences of Belarus","volume":"42 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stationary orbits of linear time-varying observation systems\",\"authors\":\"A. Astrovskii\",\"doi\":\"10.29235/1561-8323-2021-65-1-18-24\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In terms of matrix observability, the necessary and sufficient conditions are obtained for the linear timevarying observation system to have stationary orbits with respect to the linear time-varying transformation group of class C1 . The full invariant of the action of a transformation group is described. It is proved that for any matrix function A c C(T, Rn×n ), there exists such an n-vector function c(t), t c T, that the pair (A, c) is uniformly observable. The algorithm for constructing a stationary system is described.\",\"PeriodicalId\":11283,\"journal\":{\"name\":\"Doklady of the National Academy of Sciences of Belarus\",\"volume\":\"42 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-02-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Doklady of the National Academy of Sciences of Belarus\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29235/1561-8323-2021-65-1-18-24\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady of the National Academy of Sciences of Belarus","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29235/1561-8323-2021-65-1-18-24","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在矩阵可观测性方面,得到了线性时变观测系统相对于C1类线性时变变换群具有平稳轨道的充分必要条件。描述了变换群作用的完全不变量。证明了对于任意矩阵函数A c c(T, Rn×n),存在这样一个n向量函数c(T), T c T,使得(A, c)对是一致可观察的。描述了构造平稳系统的算法。
Stationary orbits of linear time-varying observation systems
In terms of matrix observability, the necessary and sufficient conditions are obtained for the linear timevarying observation system to have stationary orbits with respect to the linear time-varying transformation group of class C1 . The full invariant of the action of a transformation group is described. It is proved that for any matrix function A c C(T, Rn×n ), there exists such an n-vector function c(t), t c T, that the pair (A, c) is uniformly observable. The algorithm for constructing a stationary system is described.