The Hankel Matrix Solution to a System of Quaternion Matrix Equations

被引：0

作者：

Wang, Yun ^{[1
]}

Huang, Jingpin ^{[1
]}

Xiong, Hao ^{[1
]}

Zhang, Shanshan ^{[1
]}

机构：

[1] Guangxi Univ Nationalities, Coll Sci, Nanning 530006, Peoples R China

来源：

PROCEEDINGS OF THE 32ND 2020 CHINESE CONTROL AND DECISION CONFERENCE (CCDC 2020) | 2020年

基金：

中国国家自然科学基金;

关键词：

Quaternion Field; Quaternion Matrix Equations; Hankel Matrix; Kronecker Product; Optimal Approximation;

D O I：

暂无

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 solution of matrix equations and the optimal approximation problem play an important role in linear optimal control, parameter identification, structural vibration, aviation and other fields. Hankel matrix is kind of matrix with special structure and wide application. In this paper, the problem of Hankel constraint solution to the system [AXB CXD]=[E F] over quaternion field is discussed. By using the representation of vectors of a Hankel matrix and Kronecker product of matrices, a constrained problem will be transformed into an unconstrained equation. Then the necessary and sufficient conditions for the equations with Hankel solution as well as the expression of general solution are obtained. Meanwhile, when the solution set is nonempty, by using invariance of Frobenius norm of orthogonal matrix product, the optimal approximation solution with minimal Frobenius norm for a given Hankel matrix is derived. Finally, two numerical examples is provided to verify the algorism.

引用

页码：5204 / 5209

页数：6

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