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A controller design procedure for a class of nonlinear systems is presented. The structure of the control system corresponds to the so-called internal-model controller that, for linear systems, has exhibited good performance and stability robustness with respect to disturbances and to uncertainty in the plant parameters. The systems involved are single-input single-output and fully linearizable by coordinates transformation and state feedback. It is shown that the plant output converges to a constant reference, even under the presence of constant disturbances and parameter uncertainties, provided the closed-loop system has an asymptotically stable equilibrium point placed anywhere. This scheme does not need an explicit design of a nonlinear observer; instead, it uses the state of a plant model. A conservative stability robustness margin is estimated by applying standard results of Lyapunov theory.