On solutions of the matrix equations XF-AX=C and XF-A(X)over-bar=C

摘要

With the help of the concept of Kronecker map, an explicit solution for the matrix equation XF - AX = 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 XF - AX = C is also studied. An explicit solution for this 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) 2006 Elsevier Inc. All rights reserved.