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Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 948590, 10 pages
http://dx.doi.org/10.1155/2010/948590
Research Article

Robust Exponential Converge Controller Design for a Unified Chaotic System with Structured Uncertainties via LMI

Department of Electrical Engineering, National Chin-Yi University of Technology, Taichung 41101, Taiwan

Received 1 September 2009; Revised 23 February 2010; Accepted 21 April 2010

Academic Editor: Antonia Vecchio

Copyright © 2010 Neng-Sheng Pai and Her-Terng Yau. 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. G. Chen and X. Dong, From Chaos to Order, vol. 24 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific Publishing, River Edge, NJ, USA, 1998, Methodologies, perspectives and applications. View at Zentralblatt MATH · View at MathSciNet
  2. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Physical Review Letters, vol. 64, no. 11, pp. 1196–1199, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. G. Chen and T. Ueta, “Yet another chaotic attractor,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 9, no. 7, pp. 1465–1466, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. Lü and G. Chen, “A new chaotic attractor coined,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 3, pp. 659–661, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. Lü, G. Chen, D. Cheng, and S. Celikovsky, “Bridge the gap between the Lorenz system and the Chen system,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 12, pp. 2917–2926, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. T. L. Vincent and J. Yu, “Control of a chaotic system,” Dynamics and Control, vol. 1, no. 1, pp. 35–52, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. Luce and J.-P. Kernévez, “Controllability of Lorenz equation,” in Bifurcation and Chaos: Analysis, Algorithms, Applications (Würzburg, 1990), vol. 97 of International Series of Numerical Mathematics, pp. 257–261, Birkhäuser, Basel, Switzerland, 1991. View at Google Scholar · View at MathSciNet
  8. T. H. Yeap and N. U. Ahmed, “Feedback control of chaotic systems,” Dynamics and Control, vol. 4, no. 1, pp. 97–114, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. A. Gallegos, “Nonlinear regulation of a Lorenz system by feedback linearization techniques,” Dynamics and Control, vol. 4, no. 3, pp. 277–298, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  10. C.-C. Fuh and P.-C. Tung, “Controlling chaos using differential geometric method,” Physical Review Letters, vol. 75, no. 16, pp. 2952–2955, 1995. View at Publisher · View at Google Scholar · View at Scopus
  11. H. T. Yau, “Design of adaptive sliding mode controller for chaos synchronization with uncertainties,” Chaos, Solitons and Fractals, vol. 22, no. 2, pp. 341–347, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Feki, “An adaptive feedback control of linearizable chaotic systems,” Chaos, Solitons and Fractals, vol. 15, no. 5, pp. 883–890, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. J. Yan, “H-infinite controlling hyperchaos of the Rössler system with input nonlinearity,” Chaos, Solitons and Fractals, vol. 21, no. 2, pp. 283–293, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. Kuntanapreeda, “Chaos synchronization of unified chaotic systems via LMI,” Physics Letters, Section A, vol. 373, no. 32, pp. 2837–2840, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994. View at MathSciNet
  16. W.-J. Mao and J. Chu, “Quadratic stability and stabilization of dynamic interval systems,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 1007–1012, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  17. P. Gahinet, P. Apkarian, and M. Chilali, “Affine parameter-dependent Lyapunov functions and real parametric uncertainty,” IEEE Transactions on Automatic Control, vol. 41, no. 3, pp. 436–442, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. G. H. Yang and K.-Y. Lum, “Comparisons among robust stability criteria for linear systems with affine parameter uncertainties,” Automatica, vol. 43, no. 3, pp. 491–498, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. C. H. Lien, K.-W. Yu, Y.-F. Lin, Y.-J. Chung, and L.-Y. Chung, “Exponential convergence rate estimation for uncertain delayed neural networks of neutral type,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2491–2499, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  20. J. Lü and G. Chen, “Generating multiscroll chaotic attractors: theories, methods and applications,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 16, no. 4, pp. 775–858, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. Lü, F. Han, X. Yu, and G. Chen, “Generating 3-D multi-scroll chaotic attractors: a hysteresis series switching method,” Automatica, vol. 40, no. 10, pp. 1677–1687, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. J. Lü, S. Yu, H. Leung, and G. Chen, “Experimental verification of multidirectional multiscroll chaotic attractors,” IEEE Transactions on Circuits and Systems, vol. 53, no. 1, pp. 149–165, 2006. View at Publisher · View at Google Scholar · View at Scopus