Lyapunov method for the controlling of the two wheels inverted pendulum

In this paper, a nonlinear controller for the stabilization of the two wheels inverted pendulum is presented. Firstly, by a suitable partial feedback linearization that allows to linearize only the actuated coordinate system, we proceed to find a function Lyapunov in conjunction with LaSalle's invariance principle. Based on this candidate function, we derive a stabilizing controller in such a way that the closed-loop system is locally asymptotically stable around its unstable equilibrium point, with a computable domain attraction.