Robust stabilization of uncertain nonlinear systems by nonsmooth output feedback

We present in this paper some new results on global robust stabilization by nonsmooth output feedback, for a class of n-dimensional uncertain systems that are not smoothly stabilizable. To handle the system uncertainty effectively, a rescaling transformation with a suitable dilation is introduced. The rescaling technique, together with the nonsmooth output feedback design method developed recently, leads to a robust output feedback control scheme which achieves, under a homogeneous growth condition, global stabilization for a family of uncertain nonlinear systems with unstabilizable/undetectable linearization. The design of nonsmooth state feedback controllers and homogeneous observers does not require the precise information of the uncertain system and depends only on the knowledge of the bounding system.