多项式方程XR + QY = Φ:解的表征

1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes Pub Date : 1980-12-01 DOI:10.1109/CDC.1980.271845

E. Emre, L. Silverman

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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。

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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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1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes

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