The limits of the solutions of a nonautonomous linear delay difference equation

Consider the system of linear delay difference equations where the coefficients Aj(n) are square matrices and kj and lj are nonnegative integers. In this note, we show that if the coefficients are “small”, then every solution of the above equation tends to a constant vector as n → ∞ and the value of the limit can be characterized by a special solution of the matrix equation and the initial conditions.