Hybrid control for global stabilization of the cart-pendulum system

A globally stabilizing controller for the cart-pendulum system is designed in this paper. The design procedure consists of three parts. First, find a neighborhood of the origin in which a locally stabilizing controller can be used. Second, construct a linear controller for the cart subsystem and steer the position and velocity of the cart to the origin. The last part is to design several classes of bang-bang controllers and a switching strategy which guarantee that the trajectory of the system starting from any initial condition enters, in finite times of switching, the neighborhood where the locally stabilizing controller is effective.