A switching controller for the stabilization of the damping inverted pendulum cart system

We present a switching approach for the stabilization of the strongly damped inverted pendulum cart system, provided that the pendulum is initialized inside of the upper-half plane, and the linear viscous force is known. The control strategy uses two stabilizing controllers. The first is a nonlinear controller, devoted to bringing the pendulum very close to its unstable equilibrium point. Then, this controller switches to a second linear controller in charge of asymptotically and exponentially renders the pendulum to the origin. The stability analysis and the estimation of the attraction domain were made using Lyapunov related tools. Convincing numerical experiments were included, where some comparison among others well-known strategies were performed.