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Abstract and Applied Analysis
Volume 2011, Article ID 969674, 16 pages
http://dx.doi.org/10.1155/2011/969674
Research Article

Novel Stability Criteria of Nonlinear Uncertain Systems with Time-Varying Delay

1School of Science, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Electrical Engineering, Tsinghua University, Beijing 100084, China

Received 31 January 2011; Revised 8 May 2011; Accepted 9 May 2011

Academic Editor: Irena Rachůnková

Copyright © 2011 Yali Dong 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.

Abstract

The problem of robust exponential stabilization for dynamical nonlinear systems with uncertainties and time-varying delay is considered in the paper. By constructing the proposed Lyapunov-Krasovskii functional approach, continuous state feedback controllers are put forward, and the criteria which guarantee the exponential stabilization of the nonlinear systems with uncertainties and time-varying delay are established in terms of solutions to the standard Riccati differential equations. Furthermore, based on the Lyapunov method and the linear matrix inequality approach, the sufficient conditions of exponential stability for a class of uncertain systems with time-varying delays and nonlinear perturbations are derived. Finally, two numerical examples are given to demonstrate the validity of the results.