摘要
We in this paper derive necessary and sufficient conditions for the system of the periodic discrete-time coupled Sylvester matrix equations AkXk ＋ YkBk = Mk, CkXk＋l ＋ YkDk ---- Nk （k = 1, 2） over the quaternion algebra to be consistent in terms of ranks and generalized inverses of the coefficient matrices. We also give an expression of the general solution to the system when it is solvable. The findings of this paper generalize some known results in the literature.
We in this paper derive necessary and sufficient conditions for the system of the periodic discrete-time coupled Sylvester matrix equations AkXk ＋ YkBk = Mk, CkXk＋l ＋ YkDk ---- Nk （k = 1, 2） over the quaternion algebra to be consistent in terms of ranks and generalized inverses of the coefficient matrices. We also give an expression of the general solution to the system when it is solvable. The findings of this paper generalize some known results in the literature.
基金
This research was supported by the grant from the National Natural Science Foundation of China （11571220）.
