In this paper, a less conservative condition for the robust stability of uncertain discrete-time linear systems is proposed. The uncertain parameters, assumed to be time-invariant, are supposed to belong to convex bounded domains (polytope type uncertainty). The stability condition is formulated in terms of a set of linear matrix inequalities involving only the vertices of the polytope domain. A simple and numerically efficient feasibility test provides a set of Lyapunov matrices whose convex combination can be used to assess the stability of any dynamic matrix inside the uncertainty domain. Examples illustrate the results. (C) 2001 Elsevier Science B.V. All rights reserved.435371378