Linear uncertain systems perturbed by persistent disturbances and driven by actuators subject to band-bounded non-linearities are considered. A set of linear matrix inequality based sufficient conditions are derived for designing state feedback controllers which assure ultimate boundedness of closed-loop state trajectories. The effect of the non-linear actuators is identified to that of the considered persistent disturbances. The control purpose is to minimize the ultimate boundedness region to which the state trajectories are eventually confined, while tolerating disturbances of given or the largest magnitudes. Finally, an experimental system, an inverted pendulum on a Stewart platform making translational movement, is arranged to demonstrate the feasibility and effectiveness of the derived results.