About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 647561, 13 pages
http://dx.doi.org/10.1155/2012/647561
Research Article

Impulsive Control for the Synchronization of Chaotic Systems with Time Delay

1College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
2Department of Mathematics, Southeast University, Nanjing 210096, China

Received 21 August 2012; Accepted 9 October 2012

Academic Editor: Jinde Cao

Copyright © 2012 Ming Han 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. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. H. N. Agiza and M. T. Yassen, “Synchronization of Rossler and Chen chaotic dynamical systems using active control,” Physics Letters A, vol. 278, no. 4, pp. 191–197, 2001. View at Publisher · View at Google Scholar
  3. J. Q. Lu and J. D. Cao, “Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters,” Chaos, vol. 15, no. 4, Article ID 043901, 10 pages, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. J. Cao and J. Lu, “Adaptive synchronization of neural networks with or without time-varying delay,” Chaos, vol. 16, no. 1, Article ID 013133, 6 pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. H. Zhang, X. K. Ma, and W. Z. Liu, “Synchronization of chaotic systems with parametric uncertainty using active sliding mode control,” Chaos, Solitons and Fractals, vol. 21, no. 5, pp. 1249–1257, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. Y. Ji, C. Y. Wen, and Z. G. Li, “Impulsive synchronization of chaotic systems via linear matrix inequalities,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 16, no. 1, pp. 221–227, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Y.-W. Wang, C. Wen, Y. C. Soh, and Z. H. Guan, “Partial state impulsive synchronization of a class of nonlinear systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 19, no. 1, pp. 387–393, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. J. Q. Lu, D. W. C. Ho, and J. D. Cao, “A unified synchronization criterion for impulsive dynamical networks,” Automatica, vol. 46, no. 7, pp. 1215–1221, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. Y. Liu, S. W. Zhao, and J. Q. Lu, “A new fuzzy impulsive control of chaotic systems based on T-S fuzzy model,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 2, pp. 393–398, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. B. Wu, Y. Liu, and J. Q. Lu, “Impulsive control of chaotic systems and its applications in synchronization,” Chinese Physics B, vol. 20, no. 5, Article ID 050508, 2011. View at Publisher · View at Google Scholar
  11. B. Wu, Y. Liu, and J. Q. Lu, “New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 837–843, 2012. View at Publisher · View at Google Scholar
  12. T. Yang and L. O. Chua, “Practical stability of impulsive synchronization between two nonautonomous chaotic systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 10, no. 4, pp. 859–867, 2000. View at Scopus
  13. W. X. Xie, C. Y. Wen, and Z. G. Li, “Impulsive control for the stabilization and synchronization of Lorenz systems,” Physics Letters A, vol. 275, no. 1-2, pp. 67–72, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Y. Li, “Some new less conservative criteria for impulsive synchronization of a hyperchaotic Lorenz system based on small impulsive signals,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 713–719, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. L. Run-Zi, “Impulsive control and synchronization of a new chaotic system,” Physics Letters A, vol. 372, no. 5, pp. 648–653, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. X. Q. Wu, J. A. Lu, C. K. Tse, J. J. Wang, and J. Liu, “Impulsive control and synchronization of the Lorenz systems family,” Chaos, Solitons and Fractals, vol. 31, no. 3, pp. 631–638, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. D. Cao, D. W. C. Ho, and Y. Q. Yang, “Projective synchronization of a class of delayed chaotic systems via impulsive control,” Physics Letters A, vol. 373, no. 35, pp. 3128–3133, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. C. Hu, H. J. Jiang, and Z. D. Teng, “Fuzzy impulsive control and synchronization of general chaotic system,” Acta Applicandae Mathematicae, vol. 109, no. 2, pp. 463–485, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. M. Haeri and M. Dehghani, “Modified impulsive synchronization of hyperchaotic systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 3, pp. 728–740, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. J. Chen, H. Liu, J. A. Lu, and Q. J. Zhang, “Projective and lag synchronization of a novel hyperchaotic system via impulsive control,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 2033–2040, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. G. M. Liu and W. Ding, “Impulsive synchronization for a chaotic system with channel time-delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 958–965, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. X. Z. Liu, “Impulsive synchronization of chaotic systems subject to time delay,” Nonlinear Analysis, vol. 71, no. 12, pp. e1320–e1327, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. X. Z. Liu and Q. Wang, “Impulsive stabilization of high-order Hopfield-type neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 19, no. 1, pp. 71–79, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. X. Z. Liu, X. S. Shen, Y. Zhang, and Q. Wang, “Stability criteria for impulsive systems with time delay and unstable system matrices,” IEEE Transactions on Circuits and Systems. I, vol. 54, no. 10, pp. 2288–2298, 2007. View at Publisher · View at Google Scholar
  25. A. Khadra, X. Z. Liu, and X. S. Shen, “Analyzing the robustness of impulsive synchronization coupled by linear delayed impulses,” IEEE Transactions on Automatic Control, vol. 54, no. 4, pp. 923–928, 2009. View at Publisher · View at Google Scholar
  26. C. Li, X. Liao, and X. Zhang, “Impulsive synchronization of chaotic systems,” Chaos, vol. 15, no. 2, Article ID 023104, 5 pages, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. J. Zhou and Q. J. Wu, “Exponential stability of impulsive delayed linear differential equations,” IEEE Transactions on Circuits and Systems II, vol. 56, no. 9, pp. 744–748, 2009. View at Publisher · View at Google Scholar
  28. Q. Wang and X. Z. Liu, “Impulsive stabilization of delay differential systems via the Lyapunov-Razumikhin method,” Applied Mathematics Letters, vol. 20, no. 8, pp. 839–845, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH