Stabilization of the Cart Pendulum using a Homogeneous Controller

This manuscript addresses the problem of stabilization of a cart pendulum using a homogeneous controller. The model of the cart pendulum is composed by a combination of strict-feedback and feedforward parts. The proposed homogeneous controller allows the feedforward nonlinearities to be globally dominated. Emphasizing the simplicity of the controller's design, the methodology relies on solving a system of linear matrix inequalities. Furthermore, a finite-time bound of convergence is evaluated. The effectiveness of the proposed methodology is validated through experimental results on a real cart pendulum.