Control of the Furuta Pendulum by using a Lyapunov function

A Lyapunov based control approach is proposed for the stabilization of the under actuated Furuta pendulum. First, by a suitable partial feedback linearization that allows to linearize only the actuated coordinate of the system, it proceeds to find a candidate Lyapunov function, and them, a stabilizing controller is derived from the obtained candidate function. The proposed closed-loop system is locally and asymptotically stable around the unstable vertical equilibrium rest, with a computable domain of attraction