State observer design and stabilization control for a class of nonlinear systems†

Abstract

In this article, the design problems of full-order state observer, reduced-order state observer and dynamic output feedback stabilization control are investigated for a class of systems with nonlinear uncertainty. Inspired by Ha and Trinh (Automatica, 40, pp. 1779–1785, 2004), the nonlinear uncertainty is assumed to be a combination of a known Lipschitz nonlinear part and an unknown state-dependent part, on which there is no restriction, such as Lipschitz condition or monotonicity etc., imposed. The existence conditions and design methods of full-order and reduced-order state observers are obtained by means of linear matrix inequalities. Moreover, a dynamic output feedback control is constructively given to exponentially stabilize the closed-loop system. †This work was completed during the author's postdoctrol period in Academy of Mathematics and Systems Science, Chinese Academy of Science.