This paper deals with robust feedback linearization control of nonlinear systems with matched uncertainties and subject to constraints on the control input. The proposed approach not only finds an appropriate pole placement for the linearized system to ensure the satisfaction of input constraints, but also tries to improve the speed of response by effectively exploiting the available control authority. The procedure guarantees the satisfaction of input signal constraints based on the invariant set theorem. Simulation results on an uncertain input-constrained nonlinear spring-mass system demonstrate the effectiveness of the proposed approach in terms of both response speed and constraint satisfaction.