Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems

被引：119
|
作者：
Ding, Feng [1 ,2 ]
Zhang, Huamin [1 ]
机构：
[1] Jiangnan Univ, Minist Educ, Key Lab Adv Proc Control Light Ind, Wuxi 214122, Peoples R China
[2] Jiangnan Univ, Control Sci & Engn Res Ctr, Wuxi 214122, Peoples R China
来源：
IET CONTROL THEORY AND APPLICATIONS | 2014年 / 8卷 / 15期
基金：
中国国家自然科学基金;
关键词：
gradient methods; search problems; matrix algebra; control system analysis; convergence of numerical methods; gradient search; gradient-based iterative algorithm; coupled matrix equations; spectral radius analysis; iterative matrix; optimal convergence factor; control system; LEAST-SQUARES SOLUTIONS; MULTIVARIABLE SYSTEMS; PARAMETER-ESTIMATION; MINIMUM-NORM; IDENTIFICATION; STATE; AXB;
D O I：
10.1049/iet-cta.2013.1044
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
By constructing an objective function and using the gradient search, a gradient-based iteration is established for solving the coupled matrix equations A(i)XB(i)=F-i, i=1, 2, ..., p. The authors prove that the gradient solution is convergent for any initial values. By analysing the spectral radius of the iterative matrix, the authors obtain an optimal convergence factor. An example is provided to illustrate the effectiveness of the proposed algorithm and to testify the conclusions established in this study.
引用
收藏
页码：1588 / 1595
页数：8
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