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Discrete Dynamics in Nature and Society
Volume 2013, Article ID 793686, 9 pages
Research Article

Wirtinger-Type Inequality and the Stability Analysis of Delayed Lur'e System

1College of Computer Science and Information, GuiZhou University, Guiyang, Guizhou 550025, China
2School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou 550004, China
3College of Science, Guizhou University, Guiyang, Guizhou 550025, China

Received 11 May 2013; Revised 26 July 2013; Accepted 27 July 2013

Academic Editor: M. De la Sen

Copyright © 2013 Zixin Liu et al. 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.


This paper proposes a new delay-depended stability criterion for a class of delayed Lur'e systems with sector and slope restricted nonlinear perturbation. The proposed method employs an improved Wirtinger-type inequality for constructing a new Lyapunov functional with triple integral items. By using the convex expression of the nonlinear perturbation function, the original nonlinear Lur'e system is transformed into a linear uncertain system. Based on the Lyapunov stable theory, some novel delay-depended stability criteria for the researched system are established in terms of linear matrix inequality technique. Three numerical examples are presented to illustrate the validity of the main results.