The problems of swinging up an inverted pendulum on a cart and controlling it around the upright position have been traditionally treated as two separate problems. This paper proposes a strategy that is globally asymptotically stabilizing under actuator saturation and, in addition, locally exponentially stabilizing. The proposed methodology performs swing up and control simultaneously and uses elements from input-output linearization, energy control, and singular perturbation theory. Experimental results on a laboratory-scale setup are presented to illustrate the applicability of the method.