{"title":"多项式方程XR + QY = Φ:解的表征","authors":"E. Emre, L. Silverman","doi":"10.1109/CDC.1980.271845","DOIUrl":null,"url":null,"abstract":"We consider the solutions of the equation XR + QY + Φ. Here Q, R, Φ are given p x q, m x t and p x t polynomial matrices over a field k. X and Y are p x m and q x t polynomial matrices which are unknown. Using certain recent results on the realization of matrix fraction descriptions of transfer matrices, we give a characterization (parameterization) of all possible (X, Y) which solve this equation. This also provides a system theoretic interpretation for this equation.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"83 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The polynomial equation XR + QY = Φ: A characterization of solutions\",\"authors\":\"E. Emre, L. Silverman\",\"doi\":\"10.1109/CDC.1980.271845\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the solutions of the equation XR + QY + Φ. Here Q, R, Φ are given p x q, m x t and p x t polynomial matrices over a field k. X and Y are p x m and q x t polynomial matrices which are unknown. Using certain recent results on the realization of matrix fraction descriptions of transfer matrices, we give a characterization (parameterization) of all possible (X, Y) which solve this equation. This also provides a system theoretic interpretation for this equation.\",\"PeriodicalId\":332964,\"journal\":{\"name\":\"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes\",\"volume\":\"83 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1980-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1980.271845\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1980.271845","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
我们考虑方程XR + QY + Φ的解。这里Q R Φ是给定域k上的p x Q m x t和p x t多项式矩阵，x和Y是未知的p x m和Q x t多项式矩阵。利用最近关于转移矩阵的矩阵分数描述实现的一些结果，给出了求解该方程的所有可能(X, Y)的表征(参数化)。这也为该方程提供了系统理论解释。
The polynomial equation XR + QY = Φ: A characterization of solutions
We consider the solutions of the equation XR + QY + Φ. Here Q, R, Φ are given p x q, m x t and p x t polynomial matrices over a field k. X and Y are p x m and q x t polynomial matrices which are unknown. Using certain recent results on the realization of matrix fraction descriptions of transfer matrices, we give a characterization (parameterization) of all possible (X, Y) which solve this equation. This also provides a system theoretic interpretation for this equation.
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