Nonsmooth output feedback stabilization and tracking of a class of nonlinear systems

Abstract

This paper addresses the problem of global output feedback stabilization for a family of planar systems whose linearization is neither controllable nor observable. Moreover, the uncontrollable modes contain eigenvalues on the right-half plane. By the well-known necessary condition, such planar systems cannot be stabilized, even locally, by any smooth output feedback, and hence must be dealt with by nonsmooth output feedback. The main contribution of this work is the development of a non-Lipschitz continuous output feedback control scheme that solves the stabilization problem, without imposing the high-order growth conditions required. As a consequence, global asymptotic tracking by output feedback is shown to be possible for a class of planar systems satisfying an output-dependent growth condition, and for a family of n-dimensional systems under a linear growth condition.