- 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 2013 (2013), Article ID 548712, 8 pages
Exponential Stability of Impulsive Stochastic Functional Differential Systems with Delayed Impulses
1School of Electrical Engineering & Information, Anhui University of Technology, Ma’anshan, Anhui 243000, China
2The Institute of System Engineering, South China University of Technology, Guangzhou, Guangdong 510640, China
3School of Mathematical Science, Anhui University, Hefei, Anhui 230039, China
Received 6 December 2012; Revised 24 February 2013; Accepted 11 March 2013
Academic Editor: Cristina Pignotti
Copyright © 2013 Fengqi Yao 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.
- Z. Luo and J. Shen, “Impulsive stabilization of functional differential equations with infinite delays,” Applied Mathematics Letters, vol. 16, no. 5, pp. 695–701, 2003.
- X. Liu, “Stability of impulsive control systems with time delay,” Mathematical and Computer Modelling, vol. 39, no. 4-5, pp. 511–519, 2004.
- X. Liu and Q. Wang, “The method of Lyapunov functionals and exponential stability of impulsive systems with time delay,” Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 7, pp. 1465–1484, 2007.
- X. Liu and Q. Wang, “On stability in terms of two measures for impulsive systems of functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 326, no. 1, pp. 252–265, 2007.
- 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.
- X. Li, “New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 4194–4201, 2010.
- X. Fu and X. Li, “Razumikhin-type theorems on exponential stability of impulsive infinite delay differential systems,” Journal of Computational and Applied Mathematics, vol. 224, no. 1, pp. 1–10, 2009.
- W.-H. Chen and W. X. Zheng, “Robust stability and -control of uncertain impulsive systems with time-delay,” Automatica, vol. 45, no. 1, pp. 109–117, 2009.
- Y. Zhang and J. Sun, “Stability of impulsive functional differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 12, pp. 3665–3678, 2008.
- D. Lin, X. Li, and D. O'Regan, “Stability analysis of generalized impulsive functional differential equations,” Mathematical and Computer Modelling, vol. 55, no. 5-6, pp. 1682–1690, 2012.
- 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.
- A. Khadra, X. Z. Liu, and X. Shen, “Analyzing the robustness of impulsive synchronization coupled by linear delayed impulses,” Institute of Electrical and Electronics Engineers, vol. 54, no. 4, pp. 923–928, 2009.
- 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.
- P. Cheng, F. Deng, and Y. Peng, “Robust exponential stability and delayed-state-feedback stabilization of uncertain impulsive stochastic systems with time-varying delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 4740–4752, 2012.
- T. Yang and L. O. Chua, “Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication,” IEEE Transactions on Circuits and Systems. I, vol. 44, no. 10, pp. 976–988, 1997.
- X. Liu, “Impulsive stabilization and control of chaotic system,” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, pp. 1081–1092, 2001.
- C. Li, X. Liao, X. Yang, and T. Huang, “Impulsive stabilization and synchronization of a class of chaotic delay systems,” Chaos, vol. 15, no. 4, Article ID 043103, 9 pages, 2005.
- X. Liu and K. Rohlf, “Impulsive control of a Lotka-Volterra system,” IMA Journal of Mathematical Control and Information, vol. 15, no. 3, pp. 269–284, 1998.
- X. Liu and A. R. Willms, “Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft,” Mathematical Problems in Engineering, pp. 277–299, 1996.
- T. E. Carter, “Optimal impulsive space trajectories based on linear equations,” Journal of Optimization Theory and Applications, vol. 70, no. 2, pp. 277–297, 1991.
- N. Yu-Jun, X. Wei, and L. Hong-Wu, “Asymptotical p-moment stability of stochastic impulsive differential equations and its application in impulsive control,” Communications in Theoretical Physics, vol. 53, no. 1, pp. 110–114, 2010.
- C. Li, L. Chen, and K. Aihara, “Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks,” Chaos, vol. 18, no. 2, Article ID 023132, 11 pages, 2008.
- L. Huang and X. Mao, “Robust delayed-state-feedback stabilization of uncertain stochastic systems,” Automatica, vol. 45, no. 5, pp. 1332–1339, 2009.
- M. S. Alwan, X. Liu, and W.-C. Xie, “Existence, continuation, and uniqueness problems of stochastic impulsive systems with time delay,” Journal of the Franklin Institute, vol. 347, no. 7, pp. 1317–1333, 2010.
- S. Peng and Y. Zhang, “Razumikhin-type theorems on th moment exponential stability of impulsive stochastic delay differential equations,” Institute of Electrical and Electronics Engineers, vol. 55, no. 8, pp. 1917–1922, 2010.
- V. Lakshmikantham and X. Z. Liu, Stability Analysis in Terms of Two Measures, World Scientific, River Edge, NJ, USA, 1993.