Lyapunov Approach for the stabilization of the Inverted Spherical Pendulum

A nonlinear controller is presented for the stabilization of the spherical inverted pendulum system. The control strategy is based on the Lyapunov approach in conjunction with LaSalle's invariance principle. The proposed controller is able to bring the pendulum to the unstable upright equilibrium point with the position of the movable base at the origin. The obtained closed-loop system has a very large domain of attraction, that can be as large as desired, for any initial position of the pendulum which lies above the horizontal plane