Numerical solution to linear matrix equation by finite steps iteration

被引：18

作者：

Li, Z. -Y. ^{[1
]}

Zhou, B. ^{[2
]}

Wang, Y. ^{[1
]}

Duan, G. -R. ^{[2
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[2] Harbin Inst Technol, Ctr Control Theory & Guidance Technol, Harbin 150001, Peoples R China

来源：

IET CONTROL THEORY AND APPLICATIONS | 2010年 / 4卷 / 07期

关键词：

DESCRIPTOR SYSTEMS; SYMMETRIC SOLUTION; POLE ASSIGNMENT; OUTPUT-FEEDBACK; STATE-FEEDBACK; REGULARIZATION; ALGORITHMS; AXB;

D O I：

10.1049/iet-cta.2009.0015

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The matrix equation Sigma(l)(i=1)A(i)XB(i) = C, which contains the well-known Sylvester matrix equation and Lyapunov matrix equation as special cases, has many important applications in control system theory. This study presents an iterative algorithm to solve such linear matrix equation. It is shown that the proposed algorithm converges to the unique solution to the linear matrix equation at finite steps for arbitrary initial condition. Moreover, if the matrix equation is not consistent, the least squares solution can be obtained by alternatively solving a linear matrix equation in the same form, which can also be solved by the proposed iterative algorithm. Numerical example shows the effectiveness of the proposed approach.

引用

页码：1245 / 1253

页数：9

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