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 $$x_n=A(x_{n-k}+x_{n-k-l}),n=0,1,2,\dots ,$$ where $A$ is a $2\times 2$ real constant matrix and $k$ and $l$ are positive integers.