A Constraint System of Generalized Sylvester Quaternion Matrix Equations

By keeping in mind the great number of applications of generalized Sylvester matrix equations in systems and control theory, in this paper we establish some necessary and sufficient conditions for the solvability to a system of eight generalized Sylvester matrix equations over the quaternion algebra. The general solution to this system is also constructed when it is solvable. Moreover, an algorithm and a numerical example are also given to make the results of this paper more practical in various fields of engineering. The findings of this paper generalize previous results in the literature.