Stability conditions for linear difference system with two delays

Abstract

In this paper, we give new necessary and sufficient conditions for the asymptotic stability of a linear delay difference system with two delays xn+1 − axn + A (xn−k + xn−l ) = 0, n ∈ {0, 1, 2, …}, where A is a 2×2 constant matrix, a ∈ [−1, 1]−{0} is a real number and l, k are positive integers such that 1 ≤ l < k.