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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 825416, 14 pages
http://dx.doi.org/10.1155/2012/825416
Research Article

Robust Local Regularity and Controllability of Uncertain TS Fuzzy Descriptor Systems

1Department of Mechanical/Electrical Engineering, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung 807, Taiwan
2Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, 100 Shi-Chuan 1st Road, Kaohsiung 807, Taiwan
3Institute of System Information and Control, National Kaohsiung First University of Science and Technology, 1 University Road, Yenchao, Kaohsiung 824, Taiwan

Received 2 October 2012; Accepted 28 October 2012

Academic Editor: Jen Chih Yao

Copyright © 2012 Shinn-Horng Chen 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. 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 Google Scholar · View at Scopus
  2. R. Babuska, Fuzzy Modeling for Control, Kluwer, Boston, Mass, USA, 1998.
  3. S. S. Farinwata, D. Filev, and R. Langari, Fuzzy Control: Synthesis and Analysis, John Wiley & Sons, Chichester, UK, 2000.
  4. T. Taniguchi, K. Tanaka, and H. O. Wang, “Fuzzy descriptor systems and nonlinear model following control,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 4, pp. 442–452, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley & Sons, New York, NY, USA, 2001.
  6. Y. Wang, Q. L. Zhang, and W. Q. Liu, “Stability analysis and design for T-S fuzzy descriptor systems,” in Proceedings of the 40th IEEE Conference on Decision and Control (CDC '01), pp. 3962–3967, Orlando, Fla, USA, December 2001. View at Scopus
  7. S. C. Tong, T. Wang, Y. P. Wang, and J. T. Tang, Design and Stability Analysis of Fuzzy Control Systems, Science Press, Beijing, China, 2004.
  8. Y. Wang, Z. Q. Sun, and F. C. Sun, “Robust fuzzy control of a class of nonlinear descriptor systems with time-varying delay,” International Journal of Control, Automation and Systems, vol. 2, no. 1, pp. 76–82, 2004. View at Google Scholar · View at Scopus
  9. T.-S. Lee, Y.-H. Chen, and J. C.-H. Chuang, “Robust control design of fuzzy dynamical systems,” Applied Mathematics and Computation, vol. 164, no. 2, pp. 555–572, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. J. S. Ren and Y. S. Yang, “Robust control of chaotic system based on T-S fuzzy model,” Systems Engineering and Electronics, vol. 27, no. 3, pp. 474–478, 2005. View at Google Scholar · View at Scopus
  11. K. Y. Lian, J. J. Liou, and C. Y. Huang, “LMI-based integral fuzzy control of DC-DC converters,” IEEE Transactions on Fuzzy Systems, vol. 14, no. 1, pp. 71–80, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. Z. Li, Fuzzy Chaotic Systems: Modeling, Control and Applications, Springer, Berlin, Germany, 2006.
  13. W. H. Ho and J. H. Chou, “Design of optimal controllers for Takagi-Sugeno fuzzy-model-based systems,” IEEE Transactions on Systems, Man, and Cybernetics Part A, vol. 37, no. 3, pp. 329–339, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. W. H. Ho, J. T. Tsai, and J. H. Chou, “Robust-stable and quadratic-optimal control for TS-fuzzy-model-based control systems with elemental parametric uncertainties,” IET Control Theory and Applications, vol. 1, no. 3, pp. 731–742, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. M. R. Hsu, W. H. Ho, and J. H. Chou, “Stable and quadratic optimal control for TS fuzzy-model-based time-delay control systems,” IEEE Transactions on Systems, Man, and Cybernetics Part A, vol. 38, no. 4, pp. 933–944, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. W. H. Ho, J. T. Tsai, and J. H. Chou, “Robust quadratic-optimal control of TS-fuzzy-model-based dynamic systems with both elemental parametric uncertainties and norm-bounded approximation error,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 3, pp. 518–531, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. Z. Hidayat, Z. Lendek, R. Babuška, and B. De Schutter, “Fuzzy observer for state estimation of the METANET traffic model,” in Proceedings of the 13th International IEEE Conference on Intelligent Transportation Systems (ITSC '10), pp. 19–24, Funchal, Portugal, September 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. C. W. Chen, “Stability analysis and robustness design of nonlinear systems: an NN-based approach,” Applied Soft Computing Journal, vol. 11, no. 2, pp. 2735–2742, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. W. H. Ho, “Takagi-Sugeno fuzzy model of nonlinear HIV dynamics: chebyshev-series approach integrated with genetic algorithm,” International Journal of Innovative Computing Information and Control, vol. 8, pp. 1439–1452, 2012. View at Google Scholar
  20. G. C. Verghese, B. C. Lévy, and T. Kailath, “A generalized state-space for singular systems,” IEEE Transactions on Automatic Control, vol. 26, no. 4, pp. 811–831, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. Y. Wang, Q. L. Zhang, and X. D. Liu, “Robustness design of uncertain discrete-time fuzzy descriptor systems with guaranteed admissibility,” in Proceedings of the American Control Conference, pp. 1699–1704, Anchorage, Alaska, USA, May 2002. View at Scopus
  22. S.-W. Kau, Y.-S. Liu, C.-H. Lee, L. Hong, and C.-H. Fang, “Static output feedback fuzzy controller design for T-S fuzzy descriptor systems,” International Journal of Fuzzy Systems, vol. 6, no. 4, pp. 187–193, 2004. View at Google Scholar
  23. B. Y. Zhu, Q. L. Zhang, and K. N. Da, “State feedback robust H control for T-S fuzzy descriptor systems,” Journal of Northeastern University. Natural Science, vol. 25, no. 5, pp. 453–456, 2004. View at Google Scholar · View at Zentralblatt MATH
  24. X. Shi and Z. W. Gao, “Stability analysis for fuzzy descriptor systems,” Systems Engineering and Electronics, vol. 27, no. 6, pp. 1087–1089, 2005. View at Google Scholar · View at Scopus
  25. B.-Y. Zhu, Q.-L. Zhang, and S.-C. Tong, “Passivity control for uncertain T-S fuzzy descriptor systems,” Acta Automatica Sinica, vol. 32, no. 5, pp. 674–679, 2006. View at Google Scholar
  26. K. Tanaka, H. Ohtake, and H. O. Wang, “A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 3, pp. 333–341, 2007. View at Publisher · View at Google Scholar · View at Scopus
  27. W. H. Tian and H. G. Zhang, “Optimal guaranteed cost control of uncertain fuzzy descriptor systems with time-varying delay,” Journal of Northeastern University, vol. 29, no. 4, pp. 464–468, 2008. View at Google Scholar · View at Zentralblatt MATH
  28. J. R. Wu, “The generalized quadratically stability for a fuzzy descriptor system,” in Proceedings of the International Conference on Machine Learning and Cybernetics, pp. 855–859, Baoding, China, July 2009. View at Publisher · View at Google Scholar · View at Scopus
  29. L. Dai, Singular Control Systems, vol. 118, Springer, Berlin, Germany, 1989. View at Publisher · View at Google Scholar
  30. Y. H. Yuan and G. M. Zhang, “Research on T-S fuzzy descriptor systems: a review,” Acta Automatica Sinica, vol. 36, no. 7, pp. 901–911, 2010. View at Publisher · View at Google Scholar
  31. J. Chen and Z. Ren, “A comparison of small gain versus Lyapunov type robust stability bounds,” International Journal of Robust and Nonlinear Control, vol. 11, no. 15, pp. 1407–1414, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  32. C. H. Hsieh and J. H. Chou, “Robust stability analysis of TS-fuzzy-model-based control systems with both elemental parametric uncertainties and norm-bounded approximation error,” JSME International Journal, Series C, vol. 47, no. 2, pp. 686–693, 2004. View at Publisher · View at Google Scholar · View at Scopus
  33. C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press, New York, NY, USA, 1975.
  34. E. L. Yip and R. F. Sincovec, “Solvability, controllability, and observability of continuous descriptor systems,” IEEE Transactions on Automatic Control, vol. 26, no. 3, pp. 702–707, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  35. D. Cobb, “Controllability, observability, and duality in singular systems,” IEEE Transactions on Automatic Control, vol. 29, no. 12, pp. 1076–1082, 1984. View at Publisher · View at Google Scholar
  36. W.-H. Ho, J.-H. Chou, and C.-Y. Guo, “Parameter identification of chaotic systems using improved differential evolution algorithm,” Nonlinear Dynamics, vol. 61, no. 1-2, pp. 29–41, 2010. View at Publisher · View at Google Scholar