Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 734340, 10 pages
doi:10.1155/2010/734340
Research Article

Stability Analysis of Interconnected Fuzzy Systems Using the Fuzzy Lyapunov Method

Ken Yeh1 and Cheng-Wu Chen2

1Department of Construction Science and Technology, De-Lin Institute of Technology, No.1, Lane 380, Qingyun Rd., Tucheng, Taipei 236, Taiwan
2Department of Logistics Management, Shu-Te University, 59 Hun Shan Road, Yen Chau, Kaohsiung 82445, Taiwan

Received 10 August 2009; Accepted 4 November 2009

Academic Editor: Carlo Cattani

Copyright © 2010 Ken Yeh and Cheng-Wu Chen. 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. C. W. Chen, W. L. Chiang, and F. H. Hsiao, “Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems,” Mathematics and Computers in Simulation, vol. 66, no. 6, pp. 523–537, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Tong, S. Tong, and Q. L. Zhang, “Robust stabilization of nonlinear time-delay interconnected systems via decentralized fuzzy control,” International Journal of Innovative Computing, Information and Control, vol. 4, no. 7, pp. 1567–1582, 2008.
  3. S. Tong and Q. L. Zhang, “Decentralized output feedback fuzzy H infinity tracking control for nonlinear interconnected systems with time-delay,” International Journal of Innovative Computing, Information and Control, vol. 4, pp. 3385–3398, 2008.
  4. L. Zadeh, “Outline of new approach to the analysis of complex systems and decision processes,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 3, pp. 28–44, 1973. View at Zentralblatt MATH · View at MathSciNet
  5. 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 Zentralblatt MATH
  6. F. Amini and R. Vahdani, “Fuzzy optimal control of uncertain dynamic characteristics in tall buildings subjected to seismic excitation,” Journal of Vibration and Control, vol. 14, no. 12, pp. 1843–1867, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  7. C. W. Chen, H. L. Wang, and J. W. Lin, “Managing target the cash balance in construction firms using a fuzzy regression approach,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 17, no. 5, pp. 667–684, 2009. View at Publisher · View at Google Scholar
  8. C. W. Chen, K. Yeh, and F. R. Liu, “Adaptive fuzzy sliding mode control for seismically excited bridges with lead rubber bearing isolation,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 17, no. 5, pp. 705–727, 2009. View at Publisher · View at Google Scholar
  9. C. Y. Chen, C. W. Shen, C. W. Chen, F. R. Liu, and M. J. Jeng, “A stability criterion for time-delay tension leg platform systems subjected to external force,” China Ocean Engineering, vol. 23, no. 1, pp. 49–57, 2009.
  10. P. C. Chen, C. W. Chen, and W. L. Chiang, “GA-based modified adaptive fuzzy sliding mode controller for nonlinear systems,” Expert Systems with Applications, vol. 36, no. 3, pp. 5872–5879, 2009. View at Publisher · View at Google Scholar
  11. R. Guclu and M. Metin, “Fuzzy logic control of vibrations of a light rail transport vehicle in use in Istanbul traffic,” Journal of Vibration and Control, vol. 15, no. 9, pp. 1423–1440, 2009. View at Publisher · View at Google Scholar
  12. F. H. Hsiao, C. W. Chen, Y. W. Liang, S. D. Xu, and W. L. Chiang, “T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays,” IEEE Transactions on Circuits and Systems I, vol. 52, no. 9, pp. 1883–1893, 2005. View at Publisher · View at Google Scholar
  13. F. H. Hsiao, W. L. Chiang, C. W. Chen, et al., “Application and robustness design of fuzzy controller for resonant and chaotic systems with external disturbance,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 13, no. 3, pp. 281–295, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. T. Y. Hsieh, H. L. Wang, C. W. Chen, et al., “A new viewpoint of s-curve regression model and its application to construction management,” International Journal on Artificial Intelligence Tools, vol. 15, no. 2, pp. 131–142, 2006. View at Publisher · View at Google Scholar
  15. C. N. Ko and C. J. Wu, “A PSO-tuning method for design of fuzzy PID controllers,” Journal of Vibration and Control, vol. 14, no. 3, pp. 375–395, 2008. View at Publisher · View at Google Scholar
  16. M. L. Lin, C. W. Chen, Q. B. Wang, et al., “Fuzzy model-based assessment and monitoring of desertification using MODIS satellite imagery,” Engineering Computations, vol. 26, no. 7, pp. 745–760, 2009. View at Publisher · View at Google Scholar
  17. M. B. Trabia, J. M. Renno, and K. A. F. Moustafa, “Generalized design of an anti-swing fuzzy logic controller for an overhead crane with hoist,” Journal of Vibration and Control, vol. 14, no. 3, pp. 319–346, 2008. View at Publisher · View at Google Scholar
  18. C. H. Tsai, C. W. Chen, W. L. Chiang, and M. L. Lin, “Application of geographic information system to the allocation of disaster shelters via fuzzy models,” Engineering Computations, vol. 25, no. 1, pp. 86–100, 2008. View at Publisher · View at Google Scholar
  19. J. W. Tu, W. L. Qu, and J. Chen, “An experimental study on semi-active seismic response control of a large-span building on top of ship lift towers,” Journal of Vibration and Control, vol. 14, no. 7, pp. 1055–1074, 2008. View at Publisher · View at Google Scholar
  20. F. Zhao, J. Chen , L. Guo, and X. Li, “Neuro-fuzzy based condition prediction of bearing health,” Journal of Vibration and Control, vol. 15, no. 7, pp. 1079–1091, 2009. View at Publisher · View at Google Scholar
  21. C. W. Chen, “Modeling and control for nonlinear structural systems via a NN-based approach,” Expert Systems with Applications, vol. 36, no. 3, pp. 4765–4772, 2009. View at Publisher · View at Google Scholar
  22. C. W. Chen, “Stability conditions of fuzzy systems and its application to structural and mechanical systems,” Advances in Engineering Software, vol. 37, no. 9, pp. 624–629, 2006. View at Publisher · View at Google Scholar
  23. C. W. Chen, “The stability of an oceanic structure with T-S fuzzy models,” Mathematics and Computers in Simulation, vol. 80, no. 2, pp. 402–426, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. C. W. Chen, C. L. Lin, C. H. Tsai, et al., “A novel delay-dependent criteria for time-delay T-S fuzzy systems using fuzzy Lyapunov method,” International Journal on Artificial Intelligence Tools, vol. 16, no. 3, pp. 545–552, 2007. View at Publisher · View at Google Scholar
  25. C. W. Chen, K. Yeh, W. L. Chiang, et al., “Modeling, H∞ control and stability analysis for structural systems using Takagi-Sugeno fuzzy model,” Journal of Vibration and Control, vol. 13, no. 11, pp. 1519–1534, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  26. C. W. Chen, “Modeling and fuzzy PDC control and its application to an oscillatory TLP structure,” Mathematical Problems in Engineering, vol. 2010, 13 pages, 2010. View at Publisher · View at Google Scholar
  27. W. Wang and L. Luoh, “Stability and stabilization of fuzzy large scale systems,” IEEE Transactions on Fuzzy Systems, vol. 12, no. 3, pp. 309–315, 2004. View at Publisher · View at Google Scholar
  28. F. H. Hsiao and J. D. Hwang, “Stability analysis of fuzzy large-scale systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 32, no. 1, pp. 122–126, 2002. View at Publisher · View at Google Scholar · View at PubMed
  29. H. N. Wu and H. Y. Zhang, “Reliable H-infinity fuzzy control for a class of discrete-time nonlinear systems using multiple fuzzy Lyapunov functions,” IEEE Transactions on Circuits and Systems I, vol. 54, no. 4, pp. 357–361, 2007. View at Publisher · View at Google Scholar
  30. K. Tanaka, T. Hori, and H. O. Wang, “A multiple Lyapunov function approach to stabilization of fuzzy control systems,” IEEE Transactions on Fuzzy Systems, vol. 11, no. 4, pp. 582–589, 2003. View at Publisher · View at Google Scholar
  31. 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
  32. K. Yeh, C. Y. Chen, and C. W. Chen, “Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method,” Applied Mathematics and Computation, vol. 205, no. 2, pp. 568–577, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. C. W. Chen, W. L. Chiang, C. H. Tsai, et al., “Fuzzy Lyapunov method for stability conditions of nonlinear systems,” International Journal on Artificial Intelligence Tools, vol. 15, no. 2, pp. 163–171, 2006. View at Publisher · View at Google Scholar
  34. S. Boyd, L. El 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 Zentralblatt MATH · View at MathSciNet