Exponential stability criteria for discrete time-delay systems

In this paper, we study the exponential stability of linear discrete time-delay systems with slowly varying coefficients and nonlinear perturbations. We establish the robustness of the exponential stability in Hilbert spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. As an application of the main results, we discuss the exponential stability of a general nonlinear system. The main novelty of this work is that we always consider the exponential behavior of solutions with respect to an specific ball. Copyright (c) 2013 John Wiley & Sons, Ltd.