About this Journal Submit a Manuscript Table of Contents 
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 872826, 21 pages
doi:10.1155/2012/872826
Research Article

Robust Tracking Control for Switched Fuzzy Systems with Fast Switching Controller

Hong Yang,1 Le Zhang,1 and Xiaodong Liu2

1School of Information Engineering, Shenyang University, Shenyang 110044, China
2School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116023, China

Received 30 August 2012; Revised 27 October 2012; Accepted 12 November 2012

Academic Editor: Wudhichai Assawinchaichote

Copyright © 2012 Hong Yang 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. D. Z. Cheng, L. Guo, Y. D. Lin, and Y. Wang, “Stabilization of switched linear systems,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 661–666, 2005. View at Publisher · View at Google Scholar · View at Scopus
  2. J. Zhao and G. M. Dimirovski, “Quadratic stability of a class of switched nonlinear systems,” IEEE Transactions on Automatic Control, vol. 49, no. 4, pp. 574–578, 2004. View at Publisher · View at Google Scholar · View at Scopus
  3. G. M. Xie and L. Wang, “Necessary and sufficient conditions for controllability and observability of switched impulsive control systems,” IEEE Transactions on Automatic Control, vol. 49, no. 6, pp. 960–966, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Liu, X. Z. Liu, and W. C. Xie, “Input-to-state stability of impulsive and switching hybrid systems with time-delay,” Automatica, vol. 47, no. 5, pp. 899–908, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. R. Wang, G. P. Liu, W. Wang, D. Rees, and Y. B. Zhao, “H∞ control for networked predictive control systems based on the switched Lyapunov function method,” IEEE Transactions on Industrial Electronics, vol. 57, no. 10, pp. 3565–3571, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Wicks, P. Peleties, and R. Decarlo, “Switched controller synthesis for the quadratic stabilisation of a pair of unstable linear systems,” European Journal of Control, vol. 4, no. 2, pp. 140–147, 1998. View at Zentralblatt MATH · View at Scopus
  7. L. Dugard and E. L. Verrist, Stability and Control of Time-Delay Systems, Springer, New York, NY, USA, 1998.
  8. E. Fridman and U. Shaked, “A descriptor system approach to H∞ control of linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 253–270, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. Q. L. Han and K. Gu, “On robust stability of time-delay systems with norm-bounded uncertainty,” IEEE Transactions on Automatic Control, vol. 46, no. 9, pp. 1426–1431, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. Y. He, M. Wu, J. H. She, and G. P. Liu, “Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties,” IEEE Transactions on Automatic Control, vol. 49, no. 5, pp. 828–832, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. J. P. Richard, “Time-delay systems: an overview of some recent advances and open problems,” Automatica, vol. 39, no. 10, pp. 1667–1694, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. S. Kim, S. A. Campbell, and X. Liu, “Stability of a class of linear switching systems with time delay,” IEEE Transactions on Circuits and Systems I, vol. 53, no. 2, pp. 384–393, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. X. M. Sun, J. Zhao, and D. J. Hill, “Stability and L2-gain analysis for switched delay systems: a delay-dependent method,” Automatica, vol. 42, no. 10, pp. 1769–1774, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. D. Xie and X. Chen, “Observer-based switched control design for switched linear systems with time delay in detection of switching signal,” IET Control Theory and Applications, vol. 2, no. 5, pp. 437–445, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. G. Xie and L. Wang, “Stabilization of switched linear systems with time-delay in detection of switching signal,” Journal of Mathematical Analysis and Applications, vol. 305, no. 1, pp. 277–290, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. D. S. Du, B. Jiang, P. Shi, and S. S. Zhou, “H∞ filtering of discrete-time switched systems with state delays via switched Lyapunov function approach,” IEEE Transactions on Automatic Control, vol. 52, no. 8, pp. 1520–1525, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. Q. K. Li, J. Zhao, and G. M. Dimirovski, “Robust tracking control for switched linear systems with time-varying delays,” IET Control Theory and Applications, vol. 2, no. 6, pp. 449–457, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. H. K. Lam and F. H. F. Leung, “Fuzzy rule-based combination of linear and switching state-feedback controllers,” Fuzzy Sets and Systems, vol. 156, no. 2, pp. 153–184, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. W. J. Wang and C. H. Sun, “Relaxed stability and stabilization conditions for a T-S fuzzy discrete system,” Fuzzy Sets and Systems, vol. 156, no. 2, pp. 208–225, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. R. Palm and D. Driankov, “Fuzzy switched hybrid systems—modeling and identification,” in Proceedings of IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA), Intelligent Systems and Semiotics (ISAS), and Intelligent Control (ISIC), pp. 130–135, September 1998. View at Scopus
  21. K. Tanaka, M. Iwasaki, and H. O. Wang, “Switching control of an R/C hovercraft: stabilization and smooth switching,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 31, no. 6, pp. 853–863, 2001. View at Publisher · View at Google Scholar · View at Scopus
  22. K. Tanaka, M. Iwasaki, and H. O. Wang, “Stability and smoothness conditions for switching fuzzy systems,” in Proceedings of the American Control Conference, pp. 2474–2478, June 2000. View at Scopus
  23. K. Tanaka, M. Iwasaki, and H. O. Wang, “Stable switching fuzzy control and its application to a Hovercraft type vehicle,” in Proceedings of the 9th IEEE International Conference on Fuzzy Systems, pp. 804–809, May 2000. View at Scopus
  24. W. J. Wang, Y. J. Chen, and C. H. Sun, “Relaxed stabilization criteria for discrete-time T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 37, no. 3, pp. 551–559, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. D. J. Choi, S. S. Lee, and P. Park, “Output-feedback H∞ control of discrete-time switching fuzzy systems,” in Proceedings of the 12th IEEE International Conference on Fuzzy Systems (FUZZ '03), vol. 1, pp. 441–446, May 2003. View at Scopus
  26. D. J. Choi and P. Park, “Guaranteed cost controller design for discrete-time switching fuzzy systems,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 34, no. 1, pp. 110–119, 2004. View at Publisher · View at Google Scholar · View at Scopus
  27. H. Yang, H. Liu, G. M. Dimirovski, and J. Zhao, “Stabilization control for a class of switched fuzzy discrete-time systems,” in Proceedings of IEEE International Conference on Fuzzy Systems, pp. 1345–1350, July 2007. View at Publisher · View at Google Scholar · View at Scopus
  28. Y. M. Li, Y. Yang, and L. Li, “Adaptive backstepping fuzzy control based on type 2- fuzzy system,” Journal of Applied Mathematics, vol. 2012, Article ID 658424, 27 pages, 2012. View at Zentralblatt MATH
  29. A. V. Savkin and A. S. Matveev, “Cyclic linear differential automata: a simple class of hybrid dynamical systems,” Automatica, vol. 36, no. 5, pp. 727–734, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  30. M. Sugeno, M. F. Griffin, and A. Bastian, “Fuzzy hierarchical control of an unmanned helicopter,” in Proceedings of the 5th International Fuzzy Systems and Applications Conference (IFSA '93), pp. 1262–1265, July 1993.
  31. Q. K. Li, J. Zhao, G. M. Dimirovski, and X. J. Liu, “Tracking control for switched linear systems with time-delay: a state-dependent switching method,” Asian Journal of Control, vol. 11, no. 5, pp. 517–526, 2009. View at Publisher · View at Google Scholar · View at Scopus
  32. B. Chen, M. Wang, X. P. Liu, and P. Shi, “Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems,” Fuzzy Sets and Systems, vol. 159, no. 8, pp. 949–967, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  33. P. Liu and T. S. Chiang, “H∞ output tracking fuzzy control for nonlinear systems with time-varying delay,” Applied Soft Computing, vol. 12, no. 9, pp. 2963–2972, 2012. View at Publisher · View at Google Scholar
  34. T. S. Chiang and P. Liu, “Robust output tracking control for discrete-time nonlinear systems with time-varying delay: virtual fuzzy model LMI-based approach,” Expert Systems with Applications, vol. 39, no. 9, pp. 8239–8247, 2012. View at Publisher · View at Google Scholar
  35. L. Zhang, H. Yang, and Y. W. Jing, “Adaptive robust tracking control for a class of uncertain switched fuzzy systems,” Journal of Northeastern University, vol. 29, no. 8, pp. 1073–1076, 2008. View at Zentralblatt MATH · View at Scopus
  36. Y. Liu, G. M. Dimirovski, and J. Zhao, “Robust output feedback control for a class of uncertain switching fuzzy systems,” in Proceedings of the 17th IFAC World Congress (IFAC '08), pp. 4773–4778, July 2008. View at Publisher · View at Google Scholar · View at Scopus
  37. S. C. Tong, T. Wang, and H. X. Li, “Fuzzy robust tracking control for uncertain nonlinear systems,” International Journal of Approximate Reasoning, vol. 30, no. 2, pp. 73–90, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  38. H. O. Wang, K. Tanaka, and M. F. Griffin, “An approach to fuzzy control of nonlinear systems: stability and design issues,” IEEE Transactions on Fuzzy Systems, vol. 4, no. 1, pp. 14–23, 1996. View at Publisher · View at Google Scholar · View at Scopus