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This paper is concerned with the robust receding horizon control of constrained discrete-time nonlinear systems affected by model uncertainty. A class of uncertainties entailing norm-bounded additive state dependent and non-state-dependent uncertainties is considered. In order to robustly enforce the constraints, a technique based on constraints tightening is formulated. Moreover, it is shown that the closed-loop system, obtained with the developed RH controller, is regionally input-to-state stable with respect to the considered class of uncertainties. A simulation example shows the effectiveness of the proposed approach.