IMA Journal of Mathematical Control and Information Advance Access originally published online on August 18, 2009
IMA Journal of Mathematical Control and Information 2009 26(3):299-317; doi:10.1093/imamci/dnp017
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Reduced-order observer design for one-sided Lipschitz non-linear systems
Astronautics School, Harbin Institute of Technology, Harbin 150001, People's Republic of China and Department of Mathematics, Harbin Normal University, Harbin 150080, People's Republic of China
Department of Automation, Information Engineering School, University of Science and Technology Beijing, Beijing 100083, People's Republic of China
School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, People's Republic of China
Email: xumingyue1962{at}126.com
Received on January 14, 2009; Revision received June 29, 2009. Accepted on July 13, 2009
In this paper, the reduced-order observer design for a class of non-linear systems is investigated. Based on the one-sided Lipschitz condition, we present sufficient conditions for the existence of the reduced-order observers of the class of non-linear systems, these conditions are less conservative than those based on Lipschitz condition in literature. It should be noted that the one-sided Lipschitz condition is directly applicable to the important class of the Lipschitz non-linear systems. In considering many problems, the present paper obtains the one-sided Lipschitz constants that are significantly smaller than the classical Lipschitz constants (see Appendix). Some examples are given to illustrate effects of the proposed approach. The last example is introduced with the goal, to illustrate our proposed method to be effective for the important class of the Lipschitz non-linear systems.
Keywords: linear matrix inequality; one-sided Lipschitz condition; reduced-order observer.