The stabilization problem of a class of linear time-invariant, discrete systems with additive-type uncertainties is discussed. The dynamical system contains uncertain elements that are known to belong to prescribed compact bounding intervals. In addition, the system to be corrupted by uncertain bounded inputs is considered. A two-part switching feedback controller structure is developed in order to stabilize the uncertain dynamical system. The form of the controller (a linear part + a non-, linear part) guarantees global uniform ultimate boundedness under certain hypotheses on the bounded system uncertainties, as well as on bounded admissible additive disturbances. The performance of the uncertain system under the application of the proposed controller is compared with that using a purely linear controller. The proposed system gives superior performance.