A New Method of Solving Special Solutions of Quaternion Generalized Lyapunov Matrix Equation

被引：1
|
作者：
Liu, Zhihong [1 ,2 ]
Li, Ying [1 ,2 ]
Fan, Xueling [1 ,2 ]
Ding, Wenxv [1 ,2 ]
机构：
[1] Liaocheng Univ, Coll Math Sci, Liaocheng 252000, Shandong, Peoples R China
[2] Res Ctr Semitensor Prod Matrices Theory & Applica, Liaocheng 252000, Shandong, Peoples R China
来源：
SYMMETRY-BASEL | 2022年 / 14卷 / 06期
基金：
中国国家自然科学基金;
关键词：
quaternion; Lyapunov equation; semi-tensor product of matrices; H-representation; (skew) bisymmetric matrix; FEEDBACK STABILIZATION; H-REPRESENTATION; SYSTEMS; STATE;
D O I：
10.3390/sym14061120
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, we study the bisymmetric and skew bisymmetric solutions of quaternion generalized Lyapunov equation. With the help of semi-tensor product of matrices, some new conclusions on the expansion rules of row and column of matrix product on quaternion matrices are proposed and applied to the calculation of quaternion matrix equation. Using the H-representation method, the independent elements are extracted according to the structural characteristics of bisymmetric matrix and skew bisymmetric matrix, so as to simplify the operation process. Finally, it is compared with the real vector representation method of quaternion matrix equation to illustrate the effectiveness and superiority of the proposed method.
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页数：14
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