Some new results on a system of Sylvester-type quaternion matrix equations

In this paper, we establish a different approach for solving the system of three coupled two-sided Sylvester-type quaternion matrix equations . We give some new necessary and sufficient conditions for the existence of a solution to this system in terms of Moore-Penrose inverses of the matrices involved. We show that these new solvability conditions are equivalent with the solvability conditions which were presented in a recent paper [Linear Algebra Appl. 2016;496:549-593]. The general solution to the system is given when the solvability conditions are satisfied. Applications that are discussed include the solvability conditions and general eta-Hermitian solution to a system of quaternion matrix equations.