Solutions to matrix equations X - AXB = CY plus R and X - A(X)over-capB = CY plus R

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:343

Article

Song, Caiqin¹  Chen, Guoliang² 

[1] Univ Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China

[2] East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

关键词: Closed-form solution;    Quaternion matrix equation;    Real representation;   

DOI  :  10.1016/j.cam.2018.05.003

来源: Elsevier

【 摘 要 】

The present work proposed an alternative approach to find the closed-form solutions of the nonhomogeneous Yakubovich matrix equation X - AXB = CY + R. Based on the derived closed-form solution to the nonhomogeneous Yakubovich matrix equation, the solutions to the nonhomogeneous Yakubovich quaternion j-conjugate matrix equation X A (X) over capB = CY + R are obtained by the use of the real representation of a quaternion matrix. The existing complex representation method requires the coefficient matrix A to be a block diagonal matrix over complex field. In contrast in this publication we allow a quaternion matrix of any dimension. As an application, eigenstructure assignment problem for descriptor linear systems is considered. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free