Semi-global Output Feedback Stabilization of a Class of Non-uniformly Observable and Non-smoothly Stabilizable Systems

Abstract

The problem of semi-global stabilization by output feedback is investigated for nonlinear systems which are non-uniformly observable and non-smoothly stabilizable. Previously, it was shown that under certain restrictive conditions, global stabilization of such nonlinear systems was achievable by nonsmooth output feedback. The main contribution of this paper is to prove that in the context of semi-global control, most of the restrictive growth conditions required in the previous work can be relaxed or removed. In particular, we show that without imposing any growth condition, it is possible to achieve semi-global stabilization by nonsmooth output feedback for a chain of odd power integrators perturbed by a triangular vector field — a significant class of nonlinear systems that are known difficult to be controlled via output feedback, due to the lack of smooth stabilizability and uniform observability. Extensions to non-strictly triangular systems are also discussed in the two-dimensional case. Examples are given to demonstrate the key features of the new semi-global output feedback control schemes.