Journal of Applied Mathematics
Volume 2013 (2013), Article ID 401572, 8 pages
http://dx.doi.org/10.1155/2013/401572
Research Article

Input-to-State Stability of Singularly Perturbed Control Systems with Delays

Yongxiang Zhao,1,2 Aiguo Xiao,2 and Li Li1

1School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China
2School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China

Received 16 December 2012; Revised 9 April 2013; Accepted 14 May 2013

Academic Editor: Kang Liu

Copyright © 2013 Yongxiang Zhao 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

We study the input-to-state stability of singularly perturbed control systems with delays. By using the generalized Halanay inequality and Lyapunov functions, we derive the input-to-state stability of some classes of linear and nonlinear singularly perturbed control systems with delays.