Improvements in direct Lyapunov stabilization of underactuated, mechanical systems

A Lyapunov direct method is presented for the stabilization of underactuated, mechanical systems. The Lyapunov approach provides the tools for control law design. This work represents a continued development of previously published techniques. The major contribution of the presentation is that a method is demonstrated for assuring the positive definiteness of certain matrices associated with the formulation. A stabilization example using the rotary inverted pendulum is included.