On matrix equations X - AXF = C and X - A(X)over-barF = C

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:230

Article

Wu, Ai-Guo¹  Wang, Hao-Qian²  Duan, Guang-Ren³ 

[1] Univ Town Shenzhen, Harbin Inst Technol, Shenzhen Grad Sch, Shenzhen 518055, Peoples R China

[2] Univ Town Shenzhen, Tsinghua Univ, Grad Sch Shenzhen, Shenzhen 518055, Peoples R China

[3] Harbin Inst Technol, Ctr Control Theory & Guidance Technol, Harbin 150001, Peoples R China

关键词: Kronecker map;    Real representation;    Controllability matrix;    Observability matrix;   

DOI  :  10.1016/j.cam.2009.01.013

来源: Elsevier

【 摘 要 】

With the help of the concept of Kronecker map, an explicit solution for the matrix equation X - AXF = C is established. This solution is neatly expressed by a symmetric operator matrix, a controllability matrix and an observability matrix. In addition, the matrix equation X - A (X) over barF = C is also studied. An explicit solution for this matrix equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two observability matrices. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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