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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 760893, 6 pages
Research Article

Relative Nonlinear Measure Method to Exponential Stability of Impulsive Delayed Differential Equations

1Department of Mathematics and Information Science, Chang’an University, Xi’an 710064, China
2School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
3The 41st Institute of the Fourth Academy of CASC, Xi’an 710025, China
4School of Science, Henan University of Technology, Zhengzhou 45000, China

Received 17 February 2013; Revised 11 August 2013; Accepted 14 August 2013

Academic Editor: Abdelaziz Rhandi

Copyright © 2013 Xueli Song 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 is devoted to providing a novel method to global exponential stability of impulsive delayed differential equations. By utilizing relative nonlinear measure method, several global exponential stability criteria are presented for the impulsive delayed differential equations. Compared with the Razumikhin technique and Lyapunov function method, our method is less conservative and gives a convergence rate, and one of our stability criteria is more flexible by incorporating an adjustable matrix. An example and its simulation are provided to illustrate that our method is efficient and our results are new and correct.