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IMA Journal of Mathematical Control and Information Advance Access originally published online on September 14, 2007
IMA Journal of Mathematical Control and Information 2008 25(3):297-303; doi:10.1093/imamci/dnm024
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A note on observer for one-sided Lipschitz non-linear systems

Guang-Da Hu{dagger}

Department of Automation, Information Engineering School, University of Science and Technology Beijing, Beijing 100083, China

{dagger} Email: ghu{at}hit.edu.cn, ghuca{at}yahoo.ca

Received on January 18, 2007; Revision received May 19, 2007. Accepted on June 24, 2007

In this note, observer design of a class of non-linear systems is considered. A quasi-one-sided Lipschitz condition is introduced to estimate the influence of non-linear vector functions on the observer. Based on the quasi-one-sided Lipschitz condition, sufficient conditions for existence of observers of the class of non-linear systems are presented which are less conservative than the results based on Lipschitz condition or one-sided Lipschitz condition in literature. Furthermore, a gain matrix of the observer is given by the linear matrix inequality.

Keywords: non-linear observer; quasi-one-sided Lipschitz condition; linear matrix inequality.


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