Swinging up of the spherical pendulum

The stabilization problem for the upright position of the controlled spherical pendulum is solved in the sense that all solutions tend to the uprig position. The suggested stabilizing regulator is a passive controller derived using the speed-gradient method in combination wit h a switching condition. It is shown that a straightforward energy-ba sed passive controller of the speed-gradient type does not even solve the stabilization problem for the compact invariant set containing t he upright position.