In this paper, a design of robust discrete control with desirable quadratic stability is proposed. The design procedure is the extended discrete version of the continuous robust quadratic stabilization technique proposed by Gu et al. [K. Cu, Y.H. Chen, M.A. Zohdy, N.K. Loh, Quadratic stabilizability of uncertain systems: a two level optimization setup, Automatica 27 (1) (1991) 161-165.]. The effect of the sampling time selection, and the effect of the domain on the robustness, is examined. The presented algorithm is applied to a discrete mass spring system, and a discrete simplified car steering system to demonstrate the feasibility of the procedure, and the effect of the time sampling on the robustness. The robustness increases in both examples considered, as the sampling time decreases to some degree. (C) 2000 Elsevier Science Ltd. All rights reserved.