Interval matrix structures are ubiquitous in nature and engineering, Ordinarily, in an uncertain system there is associated with a set Of Coupled interval matrices, a basic issue of exploring its asymptotic stability. Here we introduce the notion of simultaneous Schur stability by linking the concepts of the majorant and the joint spectral radius, and prove the asymptotic stability of a set of interval matrices governed by simutaneous Schur stability. The present result may lead to the stability analysis of discrete dynamical interval systems. (C) 2008 Elsevier Ltd. All rights reserved.