Solutions to matrix equations X−AXB=CY+R and X−AX̂B=CY+R
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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−AX̂B=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.
论文关键词:Closed-form solution,Quaternion matrix equation,Real representation
论文评审过程:Received 16 February 2016, Revised 19 January 2018, Available online 9 May 2018, Version of Record 26 May 2018.
论文官网地址:https://doi.org/10.1016/j.cam.2018.05.003