A discrete-time nonlinear system model is considered. It is assumed that the model contains a parameter perturbation whose effect on the stability robustness of the controller is to be investigated. A static state feedback that achieves input-output linearization for the unperturbed system is applied. If the linearized system can be stabilized by a state estimate feedback, then it is shown under certain conditions that the state of the perturbed nonlinear system remains ultimately bounded. An example involving an application to a single-link robot is included.