Stability of a time discrete perturbed dynamical system with delay

Let Cⁿ be the set of n complex vectors endowed with a norm . Let A, B be two complex n × n matrices and τ a positive integer. In the present paper we consider the nonlinear difference equation with delay of the type

, where F_k : Cⁿ × Cⁿ → Cⁿ satisfies the condition , where p and q are positive constants. In this paper, absolute stability conditions for this equation are established.