ON THE MATRIX EQUATIONS UI XVJ = WIJ FOR 1 ≤ I, J < K WITH I plus J ≤ K

被引：0
|
作者：
van der Woude, Jacob [1 ]
机构：
[1] Delft Univ Technol, Dept Appl Math, Fac Elect Engn Math Comp Sci, NL-2600 AA Delft, Netherlands
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2016年 / 31卷
关键词：
Linear matrix equations; Common solution; Rational matrix equations; Triangular decoupling; SUBSPACES; FEEDBACK;
D O I：
10.13001/1081-3810.3312
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Conditions for the existence of a common solution X for the linear matrix equations U-i X V-j = W-ij for 1 <= i, j < k with i + j <= k. where the given matrices U-i,V-j,W-ij and the unknown matrix X have suitable dimensions, are derived. Verifiable necessary and sufficient solvability conditions, stated directly interms of the given matrices and notusing Kronecker products, are also presented. As an application, a version of the almost triangular decoupling problem is studied, and conditions for its solvability in transfer matrix and state space terms are presented.
引用
收藏
页码：465 / 475
页数：11
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