Stabilization of a class of under-actuated nonlinear systems via under-actuated back-stepping

The stabilization problem for a class of nonlinear systems is solved via a novel method inspired by back-stepping. The method, that we call under-actuated back-stepping, is introduced by solving the stabilization problem for an inertia wheel pendulum and it is then developed for a class of under-actuated mechanical systems. The properties of the resulting closed-loop systems are studied in detail and case studies are given to show the effectiveness of the proposed method.