About this Journal Submit a Manuscript Table of Contents 
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 358201, 11 pages
doi:10.1155/2012/358201
Research Article

Design of PDC Controllers by Matrix Reversibility for Synchronization of Yin and Yang Chaotic Takagi-Sugeno Fuzzy Henon Maps

Chun-Yen Ho,1 Hsien-Keng Chen,2 and Zheng-Ming Ge1

1Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan
2Department of Mechanical Engineering, Hsiuping University of Science and Technology, Dali City, Taichung 412, Taiwan

Received 6 June 2012; Revised 8 October 2012; Accepted 9 October 2012

Academic Editor: Zhenya Yan

Copyright © 2012 Chun-Yen Ho 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. H. N. Agiza, “Chaos synchronization of Lü dynamical system,” Nonlinear Analysis: Theory, Methods & Applications, vol. 58, no. 1-2, pp. 11–20, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. E. E. Escultura, “Dynamic modeling of chaos and turbulence,” Nonlinear Analysis: Theory, Methods and Applications, vol. 63, no. 5–7, pp. e519–e532, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics, John Wiley & Sons, New York, NY, USA, 1995. View at Publisher · View at Google Scholar
  4. F. Takeo, “Chaos and hypercyclicity for solution semigroups to some partial differential equations,” Nonlinear Analysis: Theory, Methods and Applications, vol. 63, no. 5–7, pp. e1943–e1953, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. Z.-M. Ge and S.-Y. Li, “Yang and Yin parameters in the Lorenz system,” Nonlinear Dynamics, vol. 62, no. 1-2, pp. 105–117, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. 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
  7. X. Huang, P. Jia, B. Liu, and L. Wang, “Chaotic particle swarm optimization for synchronization of finite dimensional Hénon dynamical system,” in Proceedings of the 6th International Conference on Natural Computation (ICNC '10), vol. 5, pp. 2600–2604, August 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. D. Arroyo, G. Alvarez, S. Li, C. Li, and J. Nunez, “Cryptanalysis of a discrete-time synchronous chaotic encryption system,” Physics Letters A, vol. 372, no. 7, pp. 1034–1039, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. Y. Xue and S. Yang, “Synchronization of discrete-time spatiotemporal chaos via adaptive fuzzy control,” Chaos, Solitons and Fractals, vol. 17, no. 5, pp. 967–973, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. B. Cazelles, G. Boudjema, and N. P. Chau, “Adaptive synchronization of globally coupled chaotic oscillators using control in noisy environments,” Physica D: Nonlinear Phenomena, vol. 103, no. 1–4, pp. 452–465, 1997. View at Scopus
  11. C.-S. Zhou and T.-L. Chen, “Robust communication via chaotic synchronization based on contraction maps,” Physics Letters A, vol. 225, no. 1–3, pp. 60–66, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man and Cybernetics, vol. 15, no. 1, pp. 116–132, 1985. View at Scopus
  13. H. Han, C. Y. Su, and S. Murakami, “Adaptive fuzzy control for a class of discrete-time nonlinear systems,” in Proceedings of the 10th IEEE International Conference on Fuzzy Systems, vol. 2, pp. 892–895, December 2001. View at Scopus
  14. K. Y. Lian, C. S. Chiu, T. S. Chiang, and P. Liu, “LMI-based fuzzy chaotic synchronization and communications,” IEEE Transactions on Fuzzy Systems, vol. 9, no. 4, pp. 539–553, 2001. View at Publisher · View at Google Scholar · View at Scopus
  15. K. Tanaka, T. Ikeda, and H. O. Wang, “A unified approach to controlling chaos via an LMI-based fuzzy control system design,” IEEE Transactions on Circuits and Systems I, vol. 45, no. 10, pp. 1021–1040, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. Y.-Y. Hou, “Controlling chaos in permanent magnet synchronous motor control system via fuzzy guaranteed cost controller,” Abstract and Applied Analysis, vol. 2012, Article ID 650863, 10 pages, 2012. View at Publisher · View at Google Scholar
  17. E. Ott, “Strange attractors and chaotic motions of dynamical systems,” Reviews of Modern Physics, vol. 53, no. 4, pp. 655–671, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. M. Hénon, “A two-dimensional mapping with a strange attractor,” Communications in Mathematical Physics, vol. 50, no. 1, pp. 69–77, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. S. Lynch, Dynamical Systems with Applications Using MATLAB, Birkhäuser, Basel, Switzerland, 2004.
  20. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, vol. 38, Springer, New York, NY, USA, 2nd edition, 1992.