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

†This work was completed during the author's postdoctrol period in Academy of Mathematics and Systems Science, Chinese Academy of Science.

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.

Keywords:

• Nonlinear uncertainty
• State observer
• Dynamic output feedback stabilization
• Linear matrix inequality

Acknowledgement

The author is grateful to the anonymous reviewers for their valuable comments and helpful suggestions. This work is supported by National Natural Science Foundation of China under Grant 60504037.

Notes

†This work was completed during the author's postdoctrol period in Academy of Mathematics and Systems Science, Chinese Academy of Science.