矩阵方程AX-EXF=BY的通解及其应用

周彬; 段广仁

引用本文:	周彬, 段广仁.矩阵方程AX-EXF=BY的通解及其应用[J].控制理论与应用,2007,24(2):193~199.[点击复制]
	ZHOU Bin, DUAN Guang-ren.General solutions to the matrix equation AX-EXF=BY and their applications[J].Control Theory and Technology,2007,24(2):193~199.[点击复制]

矩阵方程AX-EXF=BY的通解及其应用

General solutions to the matrix equation AX-EXF=BY and their applications

摘要点击 1731 全文点击 877 投稿时间：2005-06-08 修订日期：2006-04-26

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DOI编号

2007,24(2):193-199

中文关键词参数通解完全自由度右互质分解 Luenberger函数观测器参数化方法

英文关键词 parametric solutions complete degree of freedom right coprime factorization Luenberger function observer parametric approach

基金项目国家杰出青年基金资助项目(69925308).

作者	单位
周彬, 段广仁	哈尔滨工业大学控制理论与制导技术研究中心,黑龙江哈尔滨 150001

中文摘要

给出矩阵方程 AX-EXY=BY的一个完全解析的、具有显式表达式和完全自由度的参数解 (X,Y) .这里假设矩阵束 (E,A,B) 为R-能控的, F为任意的方阵.相比于现有结论,求解算法不要求矩阵A和F具有特殊的形式,且对它们的特征值没有任何的限制.此外,本文给出的通解还具有结构简洁的特点.作为一个应用,给出了广义系统正常Luenberger函数观测器的一种参数化的设计方法.算例证明了方法的有效性.

英文摘要

The problem of solving the matrix equationAX-EXY = BY is studied in this paper. Firstly,a complete general parametric expression for (X,Y) satisfying this equation is obtained. Here matrix triple (E,A,B) is R-controllable and F is an arbitrary matrix. Compared with existing results, the algorithm does not need the matrices F and A to be in any canonical forms and the knowledge of their eigenvalues. Furthermore,this type of solution has a very neat form. As a demonstration, the Luenberger function observer design of descriptor linear system is considered and a parametric design procedure is established.Finally, a numerical example shows the effectiveness of the proposed approach..