Approaches to robust H∞ controller synthesis of nonlinear discrete-time-delay systems via Takagi-Sugeno fuzzy models

Recent Advances in Intelligent Control Systems

Volumn , Issue , 2009, Pages 21-49

  Qiu, Jianbin ^a   Feng, Gang ^b   Yang, Jie ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80053062575     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-84882-548-2_2     Document Type: Chapter

References (47)

1. L. A. Zadeh, Outline of a new approach to analysis of complex systems and decision processes, IEEE Transactions on Systems, Man, Cybernetics, vol. SMC-3, no. 1, pp. 28-44, Jan. 1973.
2. M. Sugeno, Industrial Applications of Fuzzy Control. New York: Elsevier, 1985.
3. T. Takagi and M. Sugeno, Fuzzy identification of systems and its application to modeling and control, IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-15, no. 1, pp. 116-132, Jan. 1985.
4. K. Tanaka and M. Sano, A robust stabilization problem of fuzzy control systems and its applications to backing up control of a truck-trailer, IEEE Transactions on Fuzzy Systems, vol. 2, no. 2, pp. 119-134, May 1994.
5. K. Tanaka and M. Sugeno, Stability analysis and design of fuzzy control systems, Fuzzy Sets and Systems, vol. 45, no. 2, pp. 135-156, Jan. 1992.
6. 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, Jan. 1996.
7. T. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley, 2001.
8. A. Sala, T. M. Guerra, and R. Babuska, Perspectives of fuzzy systems and control, Fuzzy Sets and Systems, vol. 156, no. 3, pp. 432-444, Dec. 2005.
9. G. Feng, A survey on analysis and design of model-based fuzzy control systems, IEEE Transactions on Fuzzy Systems, vol. 14, no. 5, pp. 676-697, Oct. 2006.
10. S. G. Cao, N. W. Rees, and G. Feng, Analysis and design for a class of complex control systems, part II: fuzzy controller design, Automatica, vol. 33, no. 6, pp. 1029-1039, June 1997.
11. H. D. Tuan, P. Apkarian, T. Narikiyo, and Y. Yamamoto, Parameterized linear matrix inequality techniques in fuzzy control system design, IEEE Transactions on Fuzzy Systems, vol. 9, no. 2, pp. 324-332, Apr. 2001.
12. M. Johansson, A. Rantzer, and K.-E. Årzén, Piecewise quadratic stability of fuzzy systems, IEEE Transactions on Fuzzy Systems, vol. 7, no. 6, pp. 713-722, Dec. 1999.
13. D. J. Choi and P. Park, H∞ state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting-dependent Lyapunov functions, IEEE Transactions on Fuzzy Systems, vol. 11, no. 2, pp. 271-278, Apr. 2003.
14. G. Feng, Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions, IEEE Transactions on Fuzzy Systems, vol. 12, no. 1, pp. 22-28, Feb. 2004.
15. L. Wang and G. Feng, Piecewise H∞ controller design of discrete time fuzzy systems, IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 34, no. 1, pp. 682-686, Feb. 2004.
16. T. M. Guerra and L. Vermeiren, LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form, Automatica, vol. 40, no. 5, pp. 823-829, May 2004.
17. S. Zhou, J. Lam, and W. X. Zheng, Control design for fuzzy systems based on relaxed nonquadratic stability and H∞ performance conditions, IEEE Transactions on Fuzzy Systems, vol. 15, no. 2, pp. 188-199, Apr. 2007.
18. A. Kruszewski, R. Wang, and T. M. Guerra, Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models: a new approach, IEEE Transactions on Automatic Control, vol. 53, no. 2, pp. 606-611, Mar. 2008.
19. C.-L. Chen, G. Feng, D. Sun, and X.-P Guan, H∞ output feedback control of discrete-time fuzzy systems with application to chaos control, IEEE Transactions on Fuzzy Systems, vol. 13, no. 4, pp. 531-543, Aug. 2005.
20. H. Gao, Z. Wang, and C. Wang, Improved H∞ control of discrete-time fuzzy systems: a cone complementarity linearization approach, Information Sciences, vol. 175, no. 1-2, pp. 57-77, Sep. 2005.
21. Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee, Delay-dependent robust stabilization of uncertain state-delayed systems, International Journal of Control, vol. 74, no. 14, pp. 1447-1455, Sep. 2001.
22. 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, May 2004.
23. Y. He, Q.-G Wang, L. Xie, and C. Lin, Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE Transactions on Automatic Control, vol. 52, no. 2, pp. 293-299, Feb. 2007.
24. Y. He, Q.-G. Wang, C. Lin, and M. Wu, Delay-range-dependent stability for systems with time-varying delay, Automatica, vol. 43, no. 2, pp. 371-376, Feb. 2007.
25. H. Gao and T. Chen, New results on stability of discrete-time systems with time-varying state delays, IEEE Transactions on Automatic Control, vol. 52, no. 2, pp. 328-334, Feb. 2007.
26. H. Gao, T. Chen, and J. Lam, A new delay system approach to network-based control, Automatica, vol. 44, no. 1, pp. 39-52, Jan. 2008.
27. X. He, Z. Wang, and D. Zhou, Robust H∞ filtering for networked systems with multiple state delays, International Journal of Control, vol. 80, no. 8, pp. 1217-1232, Aug. 2007.
28. Y.-Y. Cao and P. M. Frank, Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach, IEEE Transactions on Fuzzy Systems, vol. 8, no. 2, pp. 200-211, Apr. 2000.
29. Y.-Y. Cao and P. M. Frank, Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy systems, Fuzzy Sets and Systems, vol. 124, no. 2, pp. 213-229, Dec. 2001.
30. S. Zhou and T. Li, Robust stabilization for delayed discrete-time fuzzy systems via basisdependent Lyapunov-Krasovskii functional, Fuzzy Sets and Systems, vol. 151, no. 1, pp. 139-153, Apr. 2005.
31. S. Xu and J. Lam, Robust H∞ control for uncertain discrete-time-delay fuzzy systems via output feedback, IEEE Transactions on Fuzzy Systems, vol. 13, no. 1, pp. 82-93, Feb. 2005.
32. C.-L. Chen, G. Feng, and X.-P. Guan, Delay-dependent stability analysis and controller synthesis for discrete-time T-S Fuzzy systems with time-delays, IEEE Transactions on Fuzzy Systems, vol. 13, no. 5, pp. 630-643, Oct. 2005.
33. C.-L. Chen and G. Feng, Delay-dependent piecewise control for time-delay T-S fuzzy systems with application to chaos control, In Proceedings of the 14th IEEE International Conference on Fuzzy Systems, Reno, Nevada, USA, May 2005, pp. 1056-1061.
34. S.-S. Chen, Y.-C. Chang, S.-F. Su, S.-L. Chung, and T.-T. Lee, Robust static output-feedback stabilization for nonlinear discrete-time systems with time-delay via fuzzy control approach, IEEE Transactions on Fuzzy Systems, vol. 13, no. 2, pp. 263-272, Apr. 2005.
35. C.-S. Tseng, Model reference output feedback fuzzy tracking control design for nonlinear discrete-time systems with time-delay, IEEE Transactions on Fuzzy Systems, vol. 14, no. 1, pp. 58-70, Feb. 2006.
36. H.-N. Wu, Delay-dependent stability analysis and stabilization for discrete-time fuzzy systems with state delays: a fuzzy Lyapunov-Krsovskii functional approach, IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 36, no. 4, pp. 954-962, Aug. 2006.
37. B. Zhang and S. Xu, Delay-dependent robust H∞ control for uncertain discrete-time fuzzy systems with time-varying delays, IEEE Transactions on Fuzzy Systems, to be published.
38. X.-P. Guan and C. Chen, Delay-dependent guaranteed cost control for T-S fuzzy systems with time-delays, IEEE Transactions on Fuzzy Systems, vol. 12, no. 2, pp. 236-249. Apr. 2004.
39. H.-N. Wu and H.-X. Li, New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay, IEEE Transactions on Fuzzy Systems, vol. 15, no. 3, pp. 482-493, June 2007.
40. J. Yoneyama, New delay-dependent approach to robust stability and stabilization for Takagi-Sugeno fuzzy time-delay systems, Fuzzy Sets and Systems, vol. 158, no. 20, pp. 2225-2237, Oct. 2007.
41. C. Lin, Q.-G. Wang, T. H. Lee, Y. He, and B. Chen, Observer-based H∞ control for T-S fuzzy systems with time-delay: delay-dependent design method, IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 37, no. 4, pp. 1030-1038, Aug. 2007.
42. B. Chen, X. Liu, S. Tong, and C. Lin, Guaranteed cost control of T-S fuzzy systems with state and input delays, Fuzzy Sets and Systems, vol. 158, no. 20, pp. 2251-2267, Oct. 2007.
43. X. Jiang and Q.-L. Han, Robust H∞ control for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay, IEEE Transactions on Fuzzy Systems, vol. 15, no. 2, pp. 321-331, Apr. 2007.
44. C. Abdallah, P. Dorato, F. Pérez, and D. Docampo, Controller synthesis for a class of interval plants, Automatica, vol. 31, no. 2, pp. 341-343, Feb. 1995.
45. L. Xie, Output feedback H∞ control of systems with parameter uncertainty, International Journal of Control, vol. 63, no. 4, pp. 741-750, Mar. 1996.
46. L. El Ghaoui and G. Scorletti, Control of rational systems using linear-fractional representations and linear matrix inequalities, A utomatica, vol. 32, no. 9, pp. 1273-1284, Sep. 1996.
47. L. El Ghaoui, F. Oustry, and M. Ait Rami, A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Transactions on Automatic Control, vol. 42, no. 8, pp. 1171-1176, Aug. 1997.