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In this paper, we present a delay-dependent robust model predictive control (MPC) algorithm for a class of discrete-time linear state-delayed systems subjected to polytopic-type uncertainties and input constraints. The state-feedback MPC law is calculated by minimizing an upper bound of the worst-case quadratic cost function over an infinite time horizon at each sampling instant. In contrast to existing robust MPC techniques, the main advantage of the proposed approach is that the algorithm is derived by using a descriptor model transformation of the time-delay system and by applying a result on bounding of cross products of vectors. This has significantly reduced the conservativeness. It has been shown that robust stability of the closed-loop system is guaranteed by the feasible MPC from the optimization problem. The effectiveness of the algorithm is demonstrated by a simulation.