Abstract: This paper is concerned with the problems of stability analysis and stabilization for discrete-time systems with multiple state delays and polytopic parameter uncertainties. A delay-dependent stability is first proposed by defining a new Lyapunov function. This criterion is further improved by introducing de Oliveira's parameter-dependent stability idea, which is less conservative than previous results for polytopic uncertain systems. The problem of state-feedback control is then investigated upon the proposed stability condition, where the complementary linearization idea proposed by E1 Ghaoui is employed to convert the controller design into a nonl near programming problem with linear matrix inequality constraints.