Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 672905, 8 pages
Research Article

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

Wei Xie

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

Received 17 September 2007; Accepted 10 January 2008

Academic Editor: Ondrej Dosly

Copyright © 2008 Wei Xie. 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 H 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.