Constructive immersion and invariance stabilization for a class of underactuated mechanical systems

In this paper a constructive approach to the stabilization of a desired equilibrium for a class of underactuated mechanical systems via the Immersion & Invariance methodology (I&I) is proposed. The design procedure shows that cases of mechanical systems with underactuation degree greater than one are included. This work generalizes the results recently reported by the authors, where an approach to obviate the solution of the corresponding PDEs for a class of nonlinear systems was proposed. Finally, our approach is successfully applied to the inertia wheel pendulum system and an interesting connection with the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is revealed.