New stability conditions for uncertain T-S fuzzy systems with interval time-varying delay

International Journal of Control, Automation and Systems

Volumn 10, Issue 3, 2012, Pages 490-497

  An, Jiyao ^a   Li, Tao ^a   Wen, Guilin ^a   Li, Renfa ^a  

^a HUNAN UNIVERSITY   (China)

Author keywords

Interval time varying delay; Linear matrix inequality (LMI); Lyapunov Krasovskii functional (LKF); Nonlinear system; T S fuzzy model

Indexed keywords

CONSTANT INTERVALS; FREE-WEIGHTING MATRICES; INTERVAL TIME-VARYING DELAYS; LINEAR MATRIX INEQUALITY (LMIS); LYAPUNOV-KRASOVSKII FUNCTIONALS; NUMERICAL EXAMPLE; OPTIMIZATION APPROACH; STABILITY CONDITION; STABILITY PROBLEM; SYSTEM UNCERTAINTIES; T S FUZZY SYSTEM; T-S FUZZY MODELS; TIME VARYING; TIME-VARYING DELAY; UNIFORMLY BOUNDED; UPPER AND LOWER BOUNDS; UPPER BOUND;

CONVEX OPTIMIZATION; FUZZY SYSTEMS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NONLINEAR SYSTEMS;

TIME VARYING CONTROL SYSTEMS;

EID: 84865956123     PISSN: 15986446     EISSN: 20054092     Source Type: Journal    
DOI: 10.1007/s12555-012-0305-9     Document Type: Article

References (30)

1. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its application to modeling and control," IEEE Trans. Systems Man Cybernetics, vol. 15, no. 1, pp. 116-132, 1985.
2. H. Ying, "The Takagi-Sugeno fuzzy controllers using the simplified linear control rules are nonlinear variable gain controllers," Automatica, vol. 34, no. 2, pp. 157-167, 1998. (Pubitemid 128392504)
3. M. Akar and U. Ozguner, "Decentralized techniques for the analysis and control of Takagi- Sugeno fuzzy systems," IEEE Trans. Fuzzy Systems, vol. 8, no. 6, pp. 691-704, 2000. (Pubitemid 32130571)
4. Y. Y. Cao and P. M. Frank, "Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models," Fuzzy Sets and System, vol. 124, no. 2, pp. 213-229, 2001. (Pubitemid 32842234)
5. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-delay Systems, Birkhauser, Basel, 2003.
6. R. J. Wang, W. W. Lin, and W. J. Wang, "Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems," IEEE Trans. Systems Man Cybernet. Part B, vol. 34, no. 2, pp. 1288-1292, 2004.
7. X. P. Guan and C. L. Chen, "Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays," IEEE Trans. Fuzzy Systems, vol. 12, no. 2, pp. 236-249, 2004.
8. C. G. Li, H. J. Wang, and X. F. Liao, "Delaydependent robust stability of uncertain fuzzy systems with time-varying delays," IEE Proceedings - Control Theory and Applications, vol. 151, no. 4, pp. 417-421, 2004.
9. C. H. Lien, "Further results on delay-dependent robust stability of uncertain fuzzy systems with time-varying delay," Chaos, Solitons and Fractals, vol. 28, no. 2, pp. 422-427, 2006.
10. C. Yang, Q.-L. Zhang, F. Zhang, and Z. Zhou. "Robustness analysis of descriptor systems with parameter uncertainties," Int. J. Control, Automation, Systems, vol. 8, no. 2, pp. 204-209, 2010.
11. B. Chen, X. P. Liu, and S. C. Tong, "New delaydependent stabilization conditions of T-S systems with constant delay," Fuzzy Sets and Systems, vol. 158, no. 20, pp. 2209-2224, 2007. (Pubitemid 47238186)
12. C. H. Lien, K. W. Yu, W. D. Chen, Z. L. Wan, and Y. J. Chung, "Stability criteria for uncertain Takagi-Sugeno fuzzy systems with interval timevarying delay," IET Control Theory and Applications, vol. 1, no. 3, pp. 746-769, 2007.
13. H. N. Wu and H. X. Li, "New approach to delaydependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay," IEEE Trans. Fuzzy Systems, vol. 15, no. 3, pp. 482-493, 2007.
14. Y. He, Q.-G. Wang, C. Lin, and M. Wu, "Delayrange- dependent stability for systems with timevarying delay," Automatica, vol. 43, no. 2, pp. 371-376, 2007. (Pubitemid 46037586)
15. Y. He, Q.-G. Wang, L. Xie, and C. Lin, "Further improvement of free-weighting matrices technique for systems with time-varying delay," IEEE Trans. Autom. Control, vol. 52, no. 2, pp. 293-299, 2007. (Pubitemid 46444284)
16. C. Peng, Y. C. Tian, and E. G. Tian, "Improved delay-dependent robust stabilization conditions of uncertain T-S fuzzy systems with time-varying delay," Fuzzy Sets and Systems, vol. 159, no. 20, pp. 2713-2729, 2008.
17. J. An and G. Wen, "Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach," Fuzzy Sets and Systems, vol. 185, no. 1, pp. 83-94, 2011.
18. F. Liu, M. Wu, Y. He, and R. Yokoyama, "New delay-dependent stability criteria for T-S fuzzy systems with time-varying delay," Fuzzy Sets and Systems, vol. 161, no. 15, pp. 2033-2042, 2010.
19. G. Li, J. Yang, and Y. Zeng, "BIBO Stabilization of T-S Fuzzy neutral systems by LMI Approach," International Journal of Control, Automation, Systems, vol. 8, no. 4, pp. 850-856, 2010.
20. V. B. Kolmanovskii and A. D. Myshkis, Applied Theory of Functional Differential Equations, Kluwer, 1999.
21. D. Yue, Q. L. Han, and J. Lam, "Network-based robust H∞ control of systems with uncertainty," Automatica, vol. 41, no. 6, pp. 999-1007, 2005. (Pubitemid 40556809)
22. X. Jiang and Q. Han, "Delay-dependent robust stability for uncertain linear systems with interval time-varying delay," Automatica, vol. 42, no. 6, pp. 1059-1065, 2006.
23. H. Shao, "New delay-dependent criteria for systems with interval delay," Automatica, vol. 45, no. 3, pp. 744-749, 2009.
24. X. Jiang and Q. Han, "On H∞ control for linear systems with interval time-varying delay," Automatica, vol. 41, no. 12, pp. 2099-2106, 2005. (Pubitemid 41525668)
25. E. Fridman, U. Shaked, and K. Liu, "New conditions for delay-derivative-dependent stability," Automatica, vol. 45, no. 11, pp. 2723-2727, 2009.
26. J. Sun, G. P. Liu, J. Chen, and D. Rees, "Improved delay-range-dependent stability criteria for linear systems with time-varying delays," Automatica, vol. 46, no. 2, pp. 466-470, 2010.
27. S. Boyd, L. E. Ghaoui, and E. Feron, Linear Matrix Inequality in System and Control Theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, 1994.
28. I. R. Petersen and C. V. Hollot, "A Riccati equation approach to the stabilization of uncertain linear systems," Automatica, vol. 22, no. 4, pp. 397-411, 1986.
29. J. Hale and S. Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
30. M. K. Song, J. B. Park, and Y. H. Joo, "A delay partitioning approach to delay-range-dependent stability analysis of fuzzy systems," International Journal of Control, Automation, and Systems, vol. 10, no. 1, pp. 143-149, 2012.