This paper addresses the robust stabilizability problem of linear discrete-time systems with time-varying polytopic uncertainties. A state feedback control law is proposed based on the construction of a parameter-dependent Lyapunov function. Also, it points out that the main results of Cuzzola, Geromel, and Morari (Automatica 38 (2002) 1183-1189) are incorrect and presents the corrected version of these results. (C) 2003 Elsevier Science Ltd. All rights reserved.