Discontinuous integral control for mechanical systems

For mechanical systems we present a controller able to track an unknown smooth signal, converging in finite time and by means of a continuous control signal. The control scheme is insensitive against unknown perturbations with bounded derivative. The controller consists of a non locally Lipschitz state feedback control law, and a discontinuous integral controller, that is able to estimate the unknown perturbation and to compensate for it. To complete an output feedback control a continuous observer for the velocity is added. It is shown that the closed loop consisting of state feedback, state observer and discontinuous integral controller has an equilibrium point that is globally, finite time stable, despite of perturbations with bounded derivative. The proof is based on a new smooth Lyapunov function.