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Open Access Research Article

An Equivalent LMI Representation of Bounded Real Lemma for Continuous-Time Systems

Wei Xie

Author Affiliations

College of Automation Science and Technology, South China University of Technology, Guangzhou 510641, China

Journal of Inequalities and Applications 2008, 2008:672905  doi:10.1155/2008/672905

The electronic version of this article is the complete one and can be found online at: http://www.journalofinequalitiesandapplications.com/content/2008/1/672905

Received:17 September 2007
Accepted:10 January 2008
Published:27 January 2008

© 2008 The Author(s).

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An equivalent linear matrix inequality (LMI) representation of bounded real lemma (BRL) for linear continuous-time systems is introduced. As to LTI system including polytopic-type uncertainties, by using a parameter-dependent Lyapunov function, there are several LMIs-based formulations for the analysis and synthesis of performance. All of these representations only provide us with different sufficient conditions. Compared with previous methods, this new representation proposed here provides us the possibility to obtain better results. Finally, some numerical examples are illustrated to show the effectiveness of proposed method.

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