Robust stabilization of uncertain high order systems via smooth output feedback

Abstract

We investigate the robust stabilization problem for a family of uncertain nonlinear systems with uncontrollable/unobservable linearization. To achieve global robust stabilization using a single output feedback controller, we introduce a rescaling transformation with an appropriate dilation, which turns out to be very effective in dealing with uncertainty of the system. Using this rescaling technique combined with the non-separation principle based design methods (Qian and Lin, 2002a; Yang and Lin, 2003), we develop a robust output feedback control scheme for uncertain nonlinear systems satisfying a homogeneous growth condition. Both a smooth state feedback controller and a homogeneous observer are designed for the rescaled system using only the knowledge of the bounding system rather than the uncertain system itself.