混合Sylvester矩阵方程组的通解(英文)

Solutions of a system of mixed generalized Sylvester matrix equations

得到了混合Sylvester矩阵方程组相容的一些充分必要条件.给出了这个混合Sylvester矩阵方程组的通解表达式.更进一步地,给出了这个混合Sylvester矩阵方程组解的极大极小秩.最后推广了一些重要结论.

In this paper,we derive some necessary and sufficient conditions for the existence of a solution to the system of mixed generalized Sylvester matrix equations where Ai,Bi,Cj,Dj,and Ej（i = 1,2,3,j = 1,2） are given complex matrices,and X,Y,and Z are variable matrices.We give an expression of the general solution to the above system when it is solvable.Moreover,we investigate the admissible ranks of the general solution to the system.This paper extends the known results in Wang and He’s recent paper（Wang Q W,He Z H.Solvability conditions and general solution for mixed Sylvester equations.Automatica,2013,49：2713-2719）.