On Stabilization of Classes of Nonlinear Systems with State Observers

Abstract

This paper investigates the stability of the overall closed-loop system which is composed of an originally unstable nonlinear system, a state observer and a linear gain state feedback controller. From the practical implementation point of view, only a reduced-order nonlinear state observer and a linear identity state observer are delt with. Therefore it is assumed that the observation equation is linear and the system is autonomous. Firstly, it is shown by utilizing a kind of separation properties that an unstable nonlinear system which can not be stabilized with a linear observer is able to be stabilized globally with a globally asymptotically stable reduced-order nonlinear observer. Secondly, it is pointed out that for certain classes of nonlinear systems, even a linear identity observer can be used to provide global asymptotic stability. Lyapunov methods are used for each proof, which are suggested to apply to obtaining more general stability criterion for a wider class of large-scale composite systems than presently available ones.