Regular Papers

International Journal of Control, Automation and Systems 2006; 4(4): 448-455

© The International Journal of Control, Automation, and Systems

Observer Design for A Class of UncertainState-Delayed Nonlinear Systems

Junwei Lu, Chunmei Feng, Shengyuan Xu*, and Yuming Chu

Nanjing University of Science and Technology, China

Abstract

This paper deals with the observer design problem for a class of state-delayed nonlinear systems with or without time-varying norm-bounded parameter uncertainty. The nonlinearities under consideration are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. The problem we address is the design of a nonlinear observer such that the resulting error system is globally asymptotically stable. For the case when there is no parameter uncertainty, a sufficient condition for the solvability of this problem is derived in terms of linear matrix inequalities and the explicit formula of a desired observer is given. Based on this, the robust observer design problem for the case when parameter uncertainties appear is considered and the solvability condition is also given. Both of the solvability conditions obtained in this paper are delay-dependent. A numerical example is provided to demonstrate the applicability of the proposed approach.

Keywords Linear matrix inequality, nonlinear systems, robust observer, time-delay systems, uncertain systems.

Article

Regular Papers

International Journal of Control, Automation and Systems 2006; 4(4): 448-455

Published online August 1, 2006

Copyright © The International Journal of Control, Automation, and Systems.

Observer Design for A Class of UncertainState-Delayed Nonlinear Systems

Junwei Lu, Chunmei Feng, Shengyuan Xu*, and Yuming Chu

Nanjing University of Science and Technology, China

Abstract

This paper deals with the observer design problem for a class of state-delayed nonlinear systems with or without time-varying norm-bounded parameter uncertainty. The nonlinearities under consideration are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. The problem we address is the design of a nonlinear observer such that the resulting error system is globally asymptotically stable. For the case when there is no parameter uncertainty, a sufficient condition for the solvability of this problem is derived in terms of linear matrix inequalities and the explicit formula of a desired observer is given. Based on this, the robust observer design problem for the case when parameter uncertainties appear is considered and the solvability condition is also given. Both of the solvability conditions obtained in this paper are delay-dependent. A numerical example is provided to demonstrate the applicability of the proposed approach.

Keywords: Linear matrix inequality, nonlinear systems, robust observer, time-delay systems, uncertain systems.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

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