Representation of solutions of delayed difference equations with linear parts given by pairwise permutable matrices via ZZ-transform

In the present paper, a system of nonhomogeneous linear difference equations with any finite number of constant delays and linear parts given by pairwise permutable matrices is considered. Representation of its solution is derived in a form of a matrix polynomial using the ZZ-transform. So the recent results for one and two delays, and an inductive formula for multiple delays are unified. The representation is suitable for theoretical as well as practical computations.