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This paper proposes a robust model predictive controller for linear parameter varying (LPV) systems subject to additive disturbances. The proposed controller relies on the constraint tightening method to guarantee that the MPC’s optimization problem remains feasible in the presence of additive disturbances. In order to decrease the conservativeness, the controller synthesis considers bounded parameter rate variations in the construction of the tightened constraints. Relevant features, such as recursive feasibility and stability of the LPV-MPC, are theoretically proven. Finally, the proposed controller is applied to a wheel-slip control problem and its effectiveness is shown by simulation results.