We show, in this paper, how a classical method for feedback linearization of a multivariable invertible nonlinear system, via dynamic extension and state feedback, can be robustified. The synthesis of the controller is achieved by means of a recursive procedure that, at each stage, consists in the augmentation of the system state space, to the purpose of rendering feedback-linearization possible, and in the design of a high-gain extended observer, to the purpose of estimating the state of the plant as well as the perturbations due to model uncertainties. As a result, a closed-loop system is obtained that, for any bounded set of initial conditions and any bounded input, recovers the performance that would have been obtained by means of the classical technique of feedback linearization via dynamic state feedback.