Global robust stabilization of minimum-phase nonlinear systems with uncertainty

Abstract

The problem of global stabilization via state feedback is studied for a class of minimum-phase nonlinear systems with unknown unmodelled time-varying parameters or disturbances belonging to a given compact set. Sufficient conditions are presented for the existence of a robust stabilizing state-feedback controller. The controller is constructed explicitly by using a Lyapunov-based recursive design procedure. The proposed feedback control law is a smooth function of the state, and requires information of bounding functions on the size of uncertainties. In the case where the disturbance signals represent only an unknown constant vector parameter and appear linearly in the system, an adaptive controller is developed based on similar arguments, achieving global stability with state regulation. The main results of this paper incorporate and generalize a number of robust and adaptive control schemes for global stabilization of uncertain feedback linearizable systems without zero dynamics.