Asymptotic stability conditions for a delay difference system

Abstract

In this paper we obtain some necessary and sufficient conditions for the asymptotic stability of the zero solution of a delay difference system $$ x_n = A (x_{n-k} + x_{n-k-l}),\quad n = 0, 1, 2, \dots, $$ where $A$ is a $2 \times 2$ real constant matrix and $k$ and $l$ are positive integers.