Stability and stabilization of discrete-time T-S fuzzy systems with stochastic perturbation and time-varying delay

IEEE Transactions on Fuzzy Systems

Volumn 22, Issue 1, 2014, Pages 124-138

  Yang, Xiaozhan ^a   Wu, Ligang ^a   Lam, Hak Keung ^b   Su, Xiaojie ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

Delay partitioning; stochastic perturbation; Takagi Sugeno (T S) fuzzy systems; time varying delay

Indexed keywords

EID: 84894205823     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2013.2249518     Document Type: Article

References (35)

1. K. J. Astrom, Introduction to Stochastic Control Theory. New York, USA: Academic, 1970.
2. O. Castillo and P. Melin, "A review on the design and optimization of interval type-2 fuzzy controllers, " Appl. Soft Comput., vol. 12, no. 4, pp. 1267-1278, 2012.
3. B. Ding, "Homogeneous polynomially nonquadratic stabilization of discrete-time Takagi-Sugeno systems via nonparallel distributed compensation law, " IEEE Trans. Fuzzy Syst., vol. 18, no. 5, pp. 994-1000, Oct. 2010.
4. P. Gahinet, A. Nemirovskii, A. J. Laub, and M. Chilali, LMI Control Toolbox User's Guide. Natick, MA, USA: The Math. Works Inc., 1995.
5. H. Gao, X. Liu, and J. Lam, "Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay, " IEEE Trans. Syst., Man Cybern. B, Cybern., vol. 39, no. 2, pp. 306-317, Apr. 2009.
6. F. Gouaisbaut and D. Peaucelle, "Delay-dependent stability analysis of linear time delay systems, " presented at the IFAC Workshop Time Delay Syst., L'Aquila, Italy, Jul. 2006.
7. W. Ho, S. Chen, I. Chen, J. Chou, and C. Shu, "Design of stable and quadratic-optimal static output feedback controllers for TS-fuzzy-model-based control systems: An integrative computational approach, " Int. J. Innov. Comput., Inf. Contro., vol. 8, no. 1(A), pp. 403-418, 2012.
8. H.-K. Lam, "Stability analysis of T-S fuzzy control systems using parameter-dependent Lyapunov function, " IET Control Theory Appl., vol. 3, no. 6, pp. 750-762, 2009.
9. H.-K. Lam and F. H. F. Leung, "Stability analysis of discrete-time fuzzy-model-based control systems with time delay: Time delay-independent approach, " Fuzzy Sets Syst., vol. 159, no. 8, pp. 990-1000, 2008.
10. M. Landry, S. A. Campbell, K. Morris, and C. O. Aguilar, "Dynamics of an inverted pendulum with delayed feedback control, " SIAM J. Appl. Math., vol. 4, no. 2, pp. 333-351. 2005.
11. H. Li, H. Liu, H. Gao, and P. Shi, "Reliable fuzzy control for active suspension systems with actuator delay and fault, " IEEE Trans. Fuzzy Syst., vol. 20, no. 2, pp. 342-357, Apr. 2012.
12. H. Li, J. Yu, C. Hilton, and H. Liu, "Adaptive sliding mode control for nonlinear active suspension systems using T-S fuzzy model, " IEEE Trans. Ind. Electron., DOI: 10.1109/TIE.2012.2202354.
13. T. Lin, S. Chang, and C. Hsu, "Robust adaptive fuzzy sliding mode control for a class of uncertain discrete-time nonlinear systems, " Int. J. Innov. Comput., Inf. Contro., vol. 8, no. 1(A), pp. 347-359, 2012.
14. P. Melin, Q. Mendoza, and O. Castillo, "Face recognition withan improved interval type-2 fuzzy logic Sugeno integral and modular neural networks, " IEEE Trans. Syst., Man Cybern. Part B, Cybern., vol. 41, no. 5, pp. 1001-1012, Sep. 2011.
15. X. Meng, J. Lam, B. Du, and H. Gao, "A partial delay-partitioning approach to stability analysis of discrete-time systems, " Automatica, vol. 46, no. 3, pp. 610-614, 2009.
16. S. K. Nguang, P. Shi, and S. Ding, "Fault detection for uncertain fuzzy systems: An LMI approach, " IEEE Trans. Fuzzy Syst., vol. 15, no. 6, pp. 1251-1262, Dec. 2007. (Pubitemid 350268654)
17. J. Qiu, G. Feng, and H. Gao, "Asynchronous output-feedback control of networked nonlinear systems with multiple packet dropouts: T-S fuzzy affine model-based approach, " IEEE Trans. Fuzzy Syst., vol. 19, no. 6, pp. 1014-1030, Dec. 2011.
18. ∞ output feedback control of fuzzy system models under sampled measurements, " Comput. Math. Appl., vol. 46, no. 5-6, pp. 705-717, 2003.
19. X. Su, P. Shi, L. Wu, and Y.-D. Song, "A novel approach to filter design for T-S fuzzy discrete-time systems with time-varying delay, " IEEE Trans. Fuzzy Syst., vol. 20, no. 6, pp. 1114-1129, Dec. 2012.
20. ∞ model reduction of T-S fuzzy stochastic systems, " IEEE Trans. Syst., Man Cybern. Part B, Cybern., vol. 42, no. 6, pp. 1574-1585, Dec. 2012.
21. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control, " IEEE Trans. Syst., Man Cybern., vol. SMC-15, no. 1, pp. 116-132, Jan./Feb. 1985.
22. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York, NY, USA: Wiley, 2001.
23. H. D. Tuan, P. Apkarian, T. Narikiyo, and Y. Yamamoto, "Parameterized linear matrix inequality techniques in fuzzy control system design, " IEEE Trans. Fuzzy Syst., vol. 9, no. 2, pp. 324-332, Apr. 2001. (Pubitemid 32505588)
24. Z. Wang, D. W. C. Ho, H. Dong, and H. Gao, "Robust finite-horizon control for a class of stochastic nonlinear time-varying systems subject to sensor and actuator saturations, " IEEE Trans. Autom. Control, vol. 55, no. 7, pp. 1716-1722, Jul. 2010.
25. Z. Wang, J. Lam, G. Wei, K. Fraser, and X. Liu, "Filtering for nonlinear genetic regulatory networks with stochastic disturbances, " IEEE Trans. Autom. Control, vol. 53, no. 10, pp. 2448-2457, Nov. 2008.
26. L. Wu, X. Su, P. Shi, and J. Qiu, "A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems, " IEEE Trans. Syst., Man Cybern. Part B, Cybern., vol. 41, no. 1, pp. 273-286, Feb. 2011.
27. L. Wu, X. Su, P. Shi, and J. Qiu, "Model approximation for discrete-time state-delay systems in the T-S fuzzy framework, " IEEE Trans. Fuzzy Syst., vol. 19, no. 2, pp. 366-378, Apr. 2011.
28. H. Wu, "Delay-dependent stability analysis and stabilization for discrete-time fuzzy systems with state delay: A fuzzy Lyapunov-Krasovskii functional approach, " IEEE Trans. Syst., Man Cybern. Part B, Cybern., vol. 36, no. 4, pp. 954-962, Aug. 2006. (Pubitemid 44178164)
29. S. Xu and J. Lam, "A survey of linear matrix inequality techniques in stability analysis of delay systems, " Int. J. Syst. Sci., vol. 39, no. 12, pp. 1095-1113, 2008.
30. S. Xu, J. Lam, D. W. C. Ho, and Y. Zou, "Novel global asymptotic stability criteria for delayed cellular neural networks, " IEEE Trans. Circuits Syst. Express Briefs, vol. 52, no. 6, pp. 349-353, Jun. 2005. (Pubitemid 40986454)
31. K. Yoshida and A. Higeta, "Toward stochastic explanation of a neutrally stable delayed feedback model of human balance control, " Int. J. Innov. Comput., Inf. Control, vol. 8, no. 3(B), pp. 2249-2259, 2012.
32. H. Zhang and Y. Shi, "Delay-dependent stabilization of discrete-time systems with time-varying delay via switching technique, " ASME J. Dyn. Syst. Meas. Control, vol. 134, no. 4, pp. 044503-1-044503-5, 2012.
33. ∞ filtering for discrete-time Takagi-Sugeno fuzzy systems, " IEEE Trans. Fuzzy Syst., vol. 20, no. 2, pp. 396-401, Apr. 2012.
34. X. Zhang, Z. Zhang, and G. Lu, "Fault detection for state-delay fuzzy systems subject to random communication delay, " Int. J. Innov. Comput., Inf. Control, vol. 8, no. 4, pp. 2439-2451, 2012.
35. Y. Zhao, H. Gao, J. Lam, and B. Du, "Stability and stabilization of delayed T-S fuzzy systems: A delay partitioning approach, " IEEE Trans. Fuzzy Syst., vol. 1, no. 11, pp. 750-762, Aug. 2009.