Stability analysis of nonautonomous difference systems with delaying arguments ✩

We present sufficient conditions for the stability of the nonautonomous difference system x(k + 1) = m j=0 Aj (k)x(k−j), k ∈ Z+, with m 1, when the (n×n)-matrices Aj (·) are slowly varying coefficients. The proposed approach is based on the generalization of the “freezing” method for ordinary differential equations. The stability conditions are formulated in terms of the corresponding Cauchy’s function. © 2007 Elsevier Inc. All rights reserved.