Robust stabilization of non-minimum phase nonlinear systems using extended high gain observers

A robust, stabilizing output feedback controller for systems in the normal form, which could potentially include systems with unstable zero dynamics, is presented. The control scheme adopted herein incorporates "smoothed" sliding mode control-chosen for its robustness properties as well as its ability to prescribe or constrain the motion of trajectories in the sliding phase-and an extended high gain observer to estimate one of the unknown functions. Stabilization in the case of an unknown control coefficient and uncertain constant parameters is shown.