- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 760893, 6 pages
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.
- I. Stamova, Stability Analysis of Impulsive Functional Differential Equations, Walter de Gruyter, New York, NY, USA, 2009.
- X. Song and J. Peng, “Exponential stability of equilibria of differential equations with time-dependent delay and non-Lipschitz nonlinearity,” Nonlinear Analysis, vol. 11, no. 5, pp. 3628–3638, 2010.
- W. H. Chen and W. X. Zheng, “Exponential stability of nonlinear time-delay systems with delayed impulse effects,” Automatica, vol. 47, no. 5, pp. 1075–1083, 2011.
- B. Liu, X. Liu, K. L. Teo, and Q. Wang, “Razumikhin-type theorems on exponential stability of impulsive delay systems,” IMA Journal of Applied Mathematics, vol. 71, no. 1, pp. 47–61, 2006.
- Q. Wang and X. Liu, “Exponential stability for impulsive delay differential equations by Razumikhin method,” Journal of Mathematical Analysis and Applications, vol. 309, no. 2, pp. 462–473, 2005.
- Q. Wang and X. Liu, “Impulsive stabilization of delay differential systems via the Lyapunov-Razumikhin method,” Applied Mathematics Letters, vol. 20, no. 8, pp. 839–845, 2007.
- Q. Wu, J. Zhou, and L. Xiang, “Global exponential stability of impulsive differential equations with any time delays,” Applied Mathematics Letters, vol. 23, no. 2, pp. 143–147, 2010.
- H. Qiao, J. Peng, and Z. B. Xu, “Nonlinear measures: a new approach to exponential stability analysis for Hopfield-type neural networks,” IEEE Transactions on Neural Networks, vol. 12, no. 2, pp. 360–370, 2001.
- X. Song, X. Xin, and W. Huang, “Exponential stability of delayed and impulsive cellular neural networks with partially Lipschitz continuous activation functions,” Neural Networks, vol. 29-30, pp. 80–90, 2012.
- G. Ballinger and X. Liu, “Existence and uniqueness results for impulsive delay differential equations,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 5, no. 1–4, pp. 579–591, 1999.
- J. Peng, H. Qiao, and Z. B. Xu, “A new approach to stability of neural networks with time-varying delays,” Neural Networks, vol. 15, no. 1, pp. 95–103, 2002.
- R. D. Driver, Ordinary and Delay Differential Equations, Springer, New York, NY, USA, 1977.
- T. Mori, N. Fukuma, and M. Kuwahara, “On an estimate of the decay rate for stable linear delay systems,” International Journal of Control, vol. 36, no. 1, pp. 95–97, 1982.