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This brief presents a backstepping-based controller with input saturations, applicable for the hover flight of an unmanned aerial vehicle (UAV). A dynamic model for a generic UAV is introduced that is valid for quasi-stationary conditions, with quaternion formulation of the kinematics equations. Based on this model, a backstepping design formulation is deduced for UAV hover control, and its global asymptotic stability is demonstrated. In order to cope with limitations due to reduced actuation, saturations are introduced in the control design, and the stability of the modified control solution is verified. Simulation results are presented for the hover stabilization of an airship UAV, which are demonstrative of the excellent performance of the proposed controller and illustrate its robustness in face of wind disturbances.