Journal Menu
- About this Journal
- Abstracting and Indexing
- 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 2012 (2012), Article ID 678536, 12 pages
doi:10.1155/2012/678536
Research Article
Exponential Stability of Impulsive Stochastic Functional Differential Systems
School of Mathematical Science, Anhui University, Anhui, Hefei 230039, China
Received 2 January 2012; Revised 25 February 2012; Accepted 26 February 2012
Academic Editor: Josef Diblík
Copyright © 2012 Zheng Wu 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.
Linked References
- J. Baštinec, J. Diblík, D. Y. Khusainov, and A. Ryvolová, “Exponential stability and estimation of solutions of linear differential systems of neutral type with constant coefficients,” Boundary Value Problems, vol. 2010, Article ID 956121, 20 pages, 2010. View at Zentralblatt MATH
- A.V. Shatyrko, D. Y. Khusainov, J. Diblík, J. Bastinec, and A. Ryvolova, “Estimates of perturbations of nonlinear indirect interval control system of neutral type,” Journal of Automation and Information Sciences, vol. 43, no. 1, pp. 13–28, 2011.
- S. Peng and L. Yang, “Global exponential stability of impulsive functional differential equations via Razumikhin technique,” Abstract and Applied Analysis, vol. 2010, Article ID 987372, 11 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Diblík and A. Zafer, “On stability of linear delay differential equations under Perron's condition,” Abstract and Applied Analysis, vol. 2011, Article ID 134072, 9 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Diblík, D. Y. Khusainov, I. V. Grytsay, and Z. Šmarda, “Stability of nonlinear autonomous quadratic discrete systems in the critical case,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 539087, 23 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Diblík, D. Ya. Khusainov, and I.V. Grytsay, “Stability investigation of nonlinear quadratic discrete dynamics systems in the critical case,” Journal of Physics: Conference Series, vol. 96, no. 1, Article ID 012042, 2008.
- J. Luo, “Exponential stability for stochastic neutral partial functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 355, no. 1, pp. 414–425, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- I. A. Dzhalladova, J. Baštinec, J. Diblík, and D. Y. Khusainov, “Estimates of exponential stability for solutions of stochastic control systems with delay,” Abstract and Applied Analysis, vol. 2011, Article ID 920412, 14 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- S. Janković, J. Randjelović, and M. Jovanović, “Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 355, no. 2, pp. 811–820, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- Z. Yu, “Almost surely asymptotic stability of exact and numerical solutions for neutral stochastic pantograph equations,” Abstract and Applied Analysis, vol. 2011, Article ID 143079, 14 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- X. Mao, Stochastic Differential Equations and Applications, Horwood, Chichester, UK, 1997.
- V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6, World Scientific Publishing, Teaneck, NJ, USA, 1989.
- A. Lin and L. Hu, “Existence results for impulsive neutral stochastic functional integro-differential inclusions with nonlocal initial conditions,” Computers & Mathematics with Applications, vol. 59, no. 1, pp. 64–73, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- B. Liu, “Stability of solutions for stochastic impulsive systems via comparison approach,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2128–2133, 2008. View at Publisher · View at Google Scholar
- R. Sakthivel and J. Luo, “Asymptotic stability of nonlinear impulsive stochastic differential equations,” Statistics & Probability Letters, vol. 79, no. 9, pp. 1219–1223, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- Q. Song and Z. Wang, “Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays,” Physica A, vol. 387, no. 13, pp. 3314–3326, 2008.
- X. Wang, Q. Guo, and D. Xu, “Exponential p-stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,” Mathematics and Computers in Simulation, vol. 79, no. 5, pp. 1698–1710, 2009. View at Publisher · View at Google Scholar
- H. Wu and J. Sun, “p-moment stability of stochastic differential equations with impulsive jump and Markovian switching,” Automatica, vol. 42, no. 10, pp. 1753–1759, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- L. Xu and D. Xu, “Mean square exponential stability of impulsive control stochastic system with time-varying delay,” Physics Letters A, vol. 373, no. 3, pp. 328–333, 2009.
- L. Shen and J. Sun, “p-th moment exponential stability of stochastic differential equations with impulse effect,” Science China Information Sciences, vol. 54, no. 8, pp. 1702–1711, 2011. View at Publisher · View at Google Scholar
- P. Cheng, F. Deng, and X. Dai, “Razumikhin-type theorems for asymptotic stability of impulsive stochastic functional differential systems,” Journal of Systems Science and Systems Engineering, vol. 19, no. 1, pp. 72–84, 2010.
- S. Peng and B. Jia, “Some criteria on pth moment stability of impulsive stochastic functional differential equations,” Statistics & Probability Letters, vol. 80, no. 13-14, pp. 1085–1092, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- P. Cheng and F. Deng, “Global exponential stability of impulsive stochastic functional differential systems,” Statistics & Probability Letters, vol. 80, no. 23-24, pp. 1854–1862, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Liu, X. Liu, and W.-C. Xie, “Impulsive stabilization of stochastic functional differential equations,” Applied Mathematics Letters, vol. 24, no. 3, pp. 264–269, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Liu, X. Liu, and W.-C. Xie, “Existence and uniqueness results for impulsive hybrid stochastic delay systems,” Communications on Applied Nonlinear Analysis, vol. 17, no. 3, pp. 37–53, 2010. View at Zentralblatt MATH