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Mathematical Problems in Engineering
Volume 2007, Article ID 86852, 10 pages
http://dx.doi.org/10.1155/2007/86852
Research Article

Chaos Synchronization Criteria and Costs of Sinusoidally Coupled Horizontal Platform Systems

1Department of Applied Mechanics and Engineering, Zhongshan University, Guangzhou 510275, China
2Center for Control and Optimization, South China University of Technology, Guangzhou 510640, China

Received 24 September 2006; Revised 12 December 2006; Accepted 11 February 2007

Academic Editor: José Manoel Balthazar

Copyright © 2007 Jianping Cai 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. Z.-M. Ge, T.-C. Yu, and Y.-S. Chen, “Chaos synchronization of a horizontal platform system,” Journal of Sound and Vibration, vol. 268, no. 4, pp. 731–749, 2003. View at Publisher · View at Google Scholar
  2. C.-L. Huang, Nonlinear dynamics of the horizontal platform, M.S. thesis, National Chiao Tung University, Hsinchu, Taiwan, 1996.
  3. J. A. K. Suykens, P. F. Curran, and L. O. Chua, “Master-slave synchronization using dynamic output feedback,” International Journal of Bifurcation and Chaos, vol. 7, no. 3, pp. 671–679, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. Lü, T. Zhou, and S. Zhang, “Chaos synchronization between linearly coupled chaotic systems,” Chaos, Solitons and Fractals, vol. 14, no. 4, pp. 529–541, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G.-P. Jiang, W. K.-S. Tang, and G. Chen, “A simple global synchronization criterion for coupled chaotic systems,” Chaos, Solitons and Fractals, vol. 15, no. 5, pp. 925–935, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. E. M. Elabbasy, H. N. Agiza, and M. M. El-Dessoky, “Global synchronization criterion and adaptive synchronization for new chaotic system,” Chaos, Solitons and Fractals, vol. 23, no. 4, pp. 1299–1309, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Sun and Y. Zhang, “Some simple global synchronization criterions for coupled time-varying chaotic systems,” Chaos, Solitons and Fractals, vol. 19, no. 1, pp. 93–98, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Y. Lei, W. Xu, J. Shen, and T. Fang, “Global synchronization of two parametrically excited systems using active control,” Chaos, Solitons and Fractals, vol. 28, no. 2, pp. 428–436, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. H. Park, “Stability criterion for synchronization of linearly coupled unified chaotic systems,” Chaos, Solitons and Fractals, vol. 23, no. 4, pp. 1319–1325, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. J.-G. Wang and Y. Zhao, “Chaotic synchronization of the master slave chaotic systems with different structures based on BANG-BANG control principle,” Chinese Physics Letters, vol. 22, no. 10, pp. 2508–2510, 2005. View at Publisher · View at Google Scholar
  11. J.-H. Shen, S. Chen, and J. Cai, “Chaos synchronization criterion and its optimizations for a nonlinear transducer system via linear state error feedback control,” Chinese Physics Letters, vol. 23, no. 6, pp. 1406–1409, 2006. View at Publisher · View at Google Scholar
  12. X. Wu, J. Cai, and M. Wang, “Master-slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control,” Journal of Sound and Vibration, vol. 295, no. 1-2, pp. 378–387, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Slotine and W. P. Li, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ, USA, 1991. View at Zentralblatt MATH
  14. Y. C. Kouomou and P. Woafo, “Stability and optimization of chaos synchronization through feedback coupling with delay,” Physics Letters, Section A, vol. 298, no. 1, pp. 18–28, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. C. Sarasola, F. J. Torrealdea, A. D'Anjou, and M. Graña, “Cost of synchronizing different chaotic systems,” Mathematics and Computers in Simulation, vol. 58, no. 4–6, pp. 309–327, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet