Exact stability sets for a linear difference system with diagonal delay

This paper is devoted to the stability analysis of a delay difference system of the form x n + 1 = a x n − k + b y n , y n + 1 = c x n + a y n − k , where a, b and c are real numbers and k is a positive integer. We establish some exact conditions for the zero solution of the system to be asymptotically stable.