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Mathematical Problems in Engineering
Volume 2015, Article ID 848203, 11 pages
http://dx.doi.org/10.1155/2015/848203
Research Article

A Solution for the Generalized Synchronization of a Class of Chaotic Systems Based on Output Feedback

1Instituto Politécnio Nacional-CIC, Avenida Juan de Dios Bátiz, s/n, 07738 México, DF, Mexico
2Department of Automatic Control, CINVESTAV-IPN, Avenida Instituto Politécnico Nacional 2508, 07360 México, DF, Mexico
3Faculty of Sciences, Autonomous University of Baja California, Km. 103 Carretera Tijuana-Ensenada, 22860 Ensenada, BCN, Mexico
4Instituto Politécnio Nacional-ESCOM, Avenida Juan de Dios Bátiz Esquina Miguel Othón de Mendizábal, 07738 México, DF, Mexico

Received 9 June 2015; Revised 4 September 2015; Accepted 6 September 2015

Academic Editor: Rafael Morales

Copyright © 2015 Carlos Aguilar-Ibanez 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. T. Yang and L. O. Chua, “Channel-independent chaotic secure communication,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 6, no. 12, pp. 2653–2660, 1996. View at Publisher · View at Google Scholar · View at Scopus
  2. O. I. Moskalenko, A. A. Koronovskii, and A. E. Hramov, “Generalized synchronization of chaos for secure communication: remarkable stability to noise,” Physics Letters A, vol. 374, no. 29, pp. 2925–2931, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. X. Jiang-Feng, M. Le-Quan, and C. Guan-Rong, “A chaotic communication scheme based on generalized synchronization and hash functions,” Chinese Physics Letters, vol. 21, no. 8, article 1445, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. L.-Q. Min, G.-R. Chen, X.-D. Zhang, X.-H. Zhang, and M. Yang, “Approach to generalized synchronization with application to chaos-based secure communication,” Communications in Theoretical Physics, vol. 41, no. 4, pp. 632–640, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, “Generalized synchronization of chaos: the auxiliary system approach,” Physical Review E, vol. 53, no. 5, pp. 4528–4535, 1996. View at Google Scholar · View at Scopus
  6. N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, “Generalized synchronization of chaos in directionally coupled chaotic systems,” Physical Review E, vol. 51, no. 2, pp. 980–994, 1995. View at Publisher · View at Google Scholar · View at Scopus
  7. S. S. Yang and C. K. Duan, “Generalized synchronization in chaotic systems,” Chaos, Solitons & Fractals, vol. 9, no. 10, pp. 1703–1707, 1998. View at Publisher · View at Google Scholar · View at Scopus
  8. B. R. Hunt, E. Ott, and J. A. Yorke, “Differentiable generalized synchronization of chaos,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 55, no. 4, pp. 4029–4034, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  9. A. E. Hramov and A. A. Koronovskii, “Generalized synchronization: a modified system approach,” Physical Review E, vol. 71, no. 6, Article ID 067201, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. J. R. Terry and G. D. VanWiggeren, “Chaotic communication using generalized synchronization,” Chaos, Solitons & Fractals, vol. 12, no. 1, pp. 145–152, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. A. E. Hramov and A. A. Koronovskii, “Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators,” Europhysics Letters, vol. 70, no. 2, pp. 169–175, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. G. Zhang, Z. Liu, and Z. Ma, “Generalized synchronization of different dimensional chaotic dynamical systems,” Chaos, Solitons & Fractals, vol. 32, no. 2, pp. 773–779, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Lu and Y. Xi, “Linear generalized synchronization of continuous-time chaotic systems,” Chaos, Solitons & Fractals, vol. 17, no. 5, pp. 825–831, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. A. E. Matouk, “Chaos synchronization between two different fractional systems of Lorenz family,” Mathematical Problems in Engineering, vol. 2009, Article ID 572724, 11 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Q. Bian and H. Yao, “Generalized synchronization between two complex dynamical networks with time-varying delay and nonlinear coupling,” Mathematical Problems in Engineering, vol. 2011, Article ID 978612, 15 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. Y. Li, Y. Zhao, and Z.-A. Yao, “Chaotic control and generalized synchronization for a hyperchaotic lorenz-stenflo system,” Abstract and Applied Analysis, vol. 2013, Article ID 515106, 18 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. T. Yang and L. O. Chua, “Generalized synchronization of chaos via linear transformations,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 9, no. 1, pp. 215–219, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. A. Kittel, J. Parisi, and K. Pyragas, “Generalized synchronization of chaos in electronic circuit experiments,” Physica D: Nonlinear Phenomena, vol. 112, no. 3-4, pp. 459–471, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. W. Liu, X. Qian, J. Yang, and J. Xiao, “Antisynchronization in coupled chaotic oscillators,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 354, no. 1-2, pp. 119–125, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. E. R. Kolchin, Differential Algebra & Algebraic Groups, Volume 54, Academic Press, 1973.
  21. R. Martínez-Guerra and J. L. Mata-Machuca, “Generalized synchronization via the differential primitive element,” Applied Mathematics and Computation, vol. 232, pp. 848–857, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. M. Fliess and H. Sira-Ramirez, “Control via state estimations of some nonlinear systems,” in Proceedings of the 6th IFAC Symposium on Nonlinear Control Systtems (NOLCOS '04), Stuttgart, Germany, September 2004.
  23. M. Fliess, “Generalized controller canonical forms for linear and nonlinear dynamics,” IEEE Transactions on Automatic Control, vol. 35, no. 9, pp. 994–1001, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. R. Martínez-Guerra, C. A. Pérez-Pinacho, and G. C. Gómez-Cortés, “Synchronization of chaotic liouvillian systems: an application to Chua's oscillator,” in Synchronization of Integral and Fractional Order Chaotic Systems, Understanding Complex Systems, pp. 135–151, Springer, 2015. View at Publisher · View at Google Scholar
  25. H. Sira-Ramirez and S. K. Agrawal, Differentially Flat Systems, Volume 17, CRC Press, 2004.
  26. Y.-W. Wang and Z.-H. Guan, “Generalized synchronization of continuous chaotic system,” Chaos, Solitons & Fractals, vol. 27, no. 1, pp. 97–101, 2006. View at Publisher · View at Google Scholar · View at Scopus
  27. J. L. Mata-Machuca and R. Martínez-Guerra, “Asymptotic synchronization of the Colpitts oscillator,” Computers & Mathematics with Applications, vol. 63, no. 6, pp. 1072–1078, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. H. Sira-Ramírez, A. Luviano-Juárez, and J. Cortés-Romero, “Flatness-based linear output feedback control for disturbance rejection and tracking tasks on a Chua's circuit,” International Journal of Control, vol. 85, no. 5, pp. 594–602, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus