Open Access

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

Journal of Inequalities and Applications20082008:672905

Received: 17 September 2007

Accepted: 10 January 2008

Published: 27 January 2008


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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Authors’ Affiliations

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


© Wei Xie. 2008

This article is published under license to BioMed Central Ltd. 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.