A Family of Pumping-Damping Smooth Strategies for Swinging Up a Pendulum

In this paper we present some additional results regarding the pumping-damping strategy for swinging up a pendulum introduced in [3]. Here, the family of energy functions is enlarged and the corresponding pumping-damping functions are proposed giving rise to new smooth controllers that swing up and stabilize the pendulum. Furthermore, a generalization of the stability criterion is introduced for this larger class of controllers.