A version of Matrosov's theorem for parameterized discrete-time time-varying systems is presented. The theorem is a discrete-time version of the continuous-time result in Loria et al., 2002 (delta-persistency of excitation: a necessary and sufficient condition for uniform attractivity, 2002, submitted for publication). Our result facilitates controller design for sampled-data nonlinear systems via their approximate discrete-time models. An application of the theorem to establishing uniform asymptotic stability of systems controlled by model reference adaptive controllers designed via approximate discrete-time plant models is presented. (C) 2004 Elsevier Ltd. All rights reserved.