Table of Contents Author Guidelines Submit a Manuscript
International Journal of Differential Equations
Volume 2011, Article ID 613695, 13 pages
http://dx.doi.org/10.1155/2011/613695
Research Article

Mean Square Stability of Impulsive Stochastic Differential Systems

Institute of System Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai, Shandong 264001, China

Received 4 December 2010; Revised 17 May 2011; Accepted 26 May 2011

Academic Editor: Xingfu Zou

Copyright © 2011 Shujie Yang 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

  1. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. View at Zentralblatt MATH
  2. D. D. Bainov and P. S. Simeonov, Systems with Impulse Effect: Stability, Theory and Applications, Ellis Horwood, Chichester, UK, 1989. View at Zentralblatt MATH
  3. W. H. Chen and W. X. Zheng, “Robust stability and H-control of uncertain impulsive systems with time-delay,” Automatica, vol. 45, no. 1, pp. 109–117, 2009. View at Publisher · View at Google Scholar
  4. Z. G. Li, C. B. Soh, and X. H. Xu, “Stability of impulsive differential systems,” Journal of Mathematical Analysis and Applications, vol. 216, no. 2, pp. 644–653, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. Z. G. Li, C. B. Soh, and X. H. Xu, “Robust stability of a class of hybrid dynamic uncertain systems,” International Journal of Robust and Nonlinear Control, vol. 8, no. 12, pp. 1059–1072, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. Z. G. Li, C. Y. Wen, and Y. C. Soh, “Analysis and design of impulsive control systems,” IEEE Transactions on Automatic Control, vol. 46, no. 6, pp. 894–897, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. T. Yang, Impulsive Systems and Control: Theory and Applications, Nova Science, New York, NY, USA, 2001.
  8. B. Autonio and B. Alfonso, “Delay-dependent stability of reset systems,” Automatica, vol. 46, no. 1, pp. 216–221, 2010. View at Publisher · View at Google Scholar
  9. J. Yang, S. M. Zhong, and W. P. Luo, “Mean square stability analysis of impulsive stochastic differential equations with delays,” Journal of Computational and Applied Mathematics, vol. 216, no. 2, pp. 474–483, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. W. H. Chen, F. Chen, and X. M. Lu, “Exponential stability of a class of singularly perturbed stochastic time-delay systems with impulse effect,” Nonlinear Analysiis: Real World Applications, vol. 11, no. 5, pp. 3463–3478, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. X. R. Mao, N. Koroleva, and A. Rodkina, “Robust stability of uncertain stochastic differential delay equations,” Systems & Control Letters, vol. 35, no. 5, pp. 325–336, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. B. Shi, D. C. Zhang, and M. J. Gai, Theory and Applications of Differential Equations, National Defence Industy Press, Beijing, China, 2005.