Further studies on control synthesis of discrete-time T-S fuzzy systems via augmented multi-indexed matrix approach

IEEE Transactions on Cybernetics

Volumn 44, Issue 12, 2014, Pages 2784-2791

  Xie, Xiangpeng ^a   Yue, Dong ^a,b   Ma, Tiedong ^c   Zhu, Xunlin ^d  

^a NANJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

^b HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c CHONGQING UNIVERSITY   (China)

^d ZHENGZHOU UNIVERSITY   (China)

Author keywords

Discrete time system; multi indexed matrix; nonparallel distributed compensation; slack variable technique; Takagi Sugeno (T S) fuzzy model

Indexed keywords

DIGITAL CONTROL SYSTEMS; FUZZY SYSTEMS; MATRIX ALGEBRA; NUMERICAL METHODS; QUALITY CONTROL;

ALGEBRAIC PROPERTIES; DISCRETE - TIME SYSTEMS; DISCRETE-TIME T-S FUZZY SYSTEMS; PARAMETER DEPENDENTS; QUALITY OF CONTROLS; SLACK VARIABLES; TAKAGI SUGENO FUZZY MODELS; TAKAGI SUGENO FUZZY SYSTEMS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 84912025946     PISSN: 21682267     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCYB.2014.2316491     Document Type: Article

References (30)

1. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control, " IEEE Trans. Syst., Man, Cybern., vol. 15, no. 1, pp. 116-132, Jan./Feb. 1985.
2. H. O. Wang, K. Tanaka, and M. F. Griffin, "An approach to fuzzy control of nonlinear systems: Stability and design issues, " IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14-23, Feb. 1996.
3. S. Jafarzadeh and M. S. Fadali, "On the stability and control of continuous-time TSK fuzzy systems, " IEEE Trans. Cybern., vol. 43, no. 3, pp. 1073-1087, Jun. 2013.
4. H. Dong, Z. Wang, J. Lam, and H. Gao, "Fuzzy-model-based robust fault detection with stochastic mixed time delays and successive packet dropouts, " IEEE Trans. Syst., Man, Cybern., B, Cybern., vol. 42, no. 2, pp. 365-376, Apr. 2012.
5. E. Kim and H. Lee, "New approaches to relaxed quadratic stability condition of fuzzy control systems, " IEEE Trans. Fuzzy Syst., vol. 8, no. 5, pp. 523-534, Oct. 2000.
6. X. D. Liu and Q. L. Zhang, "New approaches to controller designs based on fuzzy observers for T-S fuzzy systems via LMI, " Automatica, vol. 39, no. 9, pp. 1571-1582, 2003.
7. C. H. Fang, Y. S. Liu, S. W. Kau, L. Hong, and C. H. Lee, "A new LMIbased approach to relaxed quadratic stabilization of T-S fuzzy control systems, " IEEE Trans. Fuzzy Syst., vol. 14, no. 3, pp. 386-397, Jun. 2006.
8. A. Sala and C. Arino, "Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem, " Fuzzy Sets Syst., vol. 158, no. 24, pp. 2671-2686, 2007.
9. V. F. Montagner, R. C. L. F. Oliveira, and P. L. D. Peres, "Convergent LMI relaxations for quadratic stabilizability and H∞ control of Takagi- Sugeno fuzzy systems, " IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 863-873, Aug. 2009.
10. M. Johansson, A. Rantzer, and K. Arzen, "Piecewise quadratic stability of fuzzy systems, " IEEE Trans. Fuzzy Syst., vol. 7, no. 6, pp. 713-722, Dec. 1999.
11. G. Feng, "Controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions, " IEEE Trans. Fuzzy Syst., vol. 11, no. 5, pp. 605-612, Oct. 2003.
12. G. Feng, C. Chen, D. Sun, and Y. Zhu, "H∞ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities, " IEEE Trans. Fuzzy Syst., vol. 13, no. 1, pp. 94-103, Feb. 2005.
13. 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, 2004.
14. B. C. Ding, H. X. Sun, and P. Yang, "Further studies on LMIbased relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno's form, " Automatica, vol. 42, no. 3, pp. 503-508, 2006.
15. B. C. Ding, "Stabilization of Takagi-Sugeno model via nonparallel distributed compsensation law, " IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 188-194, Feb. 2010.
16. H. Zhang and X. Xie, "Relaxed stability conditions for continuoustime T-S fuzzy control systems via augmented multi-indexed matrix approach, " IEEE Trans. Fuzzy Syst., vol. 19, no. 3, pp. 478-492, Jun. 2011.
17. J. Pan, S. Fei, A. Jaadari, and T. M. Guerra, "Nonquadratic stabilization of continuous T-S fuzzy models: LMI solution for local approach, " IEEE Trans. Fuzzy Syst., vol. 20, no. 3, pp. 594-602, Jun. 2012.
18. D. H. Lee, J. B. Park, and Y. H. Joo, "Approaches to extended non-quadratic stability and stabilization conditions for discretetime Takagi-Sugeno fuzzy systems, " Automatica, vol. 47, no. 3, pp. 534-538, 2011.
19. A. Kruszewski, R. Wang, and T. M. Guerra, "Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete-time T-S fuzzy models: A new approach, " IEEE Trans. Autom. Control, vol. 53, no. 2, pp. 606-611, Mar. 2008.
20. T. M. Guerra, A. Kruszewski, and M. Bernal, "Control law proposition for the stabilization of discrete Takagi-Sugeno models, " IEEE Trans. Fuzzy Syst., vol. 17, no. 3, pp. 724-731, Jun. 2009.
21. D. H. Lee, J. B. Park, and Y. H. Joo, "Further improvement of periodic control approach for relaxed stabilization condition of discretetime Takagi-Sugeno fuzzy systems, " Fuzzy Sets Syst., vol. 174, no. 1, pp. 50-65, 2011.
22. R. C. L. F. Oliveira and P. L. D. Peres, "Parameter-dependent LMIs in robust analysis: Characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations, " IEEE Trans. Autom. Control, vol. 52, no. 7, pp. 1334-1340, Jul. 2007.
23. D. H. Lee, J. B. Park, and Y. H. Joo, "Improvement on nonquadratic stabilization of discrete-time Takagi-Sugeno fuzzy systems: Multipleparameterization approach, " IEEE Trans. Fuzzy Syst., vol. 18, no. 2, pp. 425-429, Apr. 2010.
24. B. C. Ding and T. Zou, "Asymptotically necessary and sufficient stability with respect to nonquadratic Lyapunov function for Takagi-Sugeno model, " in Proc. Joint 48th IEEE CDC, 28th CCD, Shanghai, China, Dec. 2009, pp. 4162-4167.
25. B. C. 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.
26. H. Zhang, X. Xie, and S. Tong, "Homogenous polynomially parameterdependent H∞ filter designs of discrete-time fuzzy systems, " IEEE Trans. Syst., Man, Cybern., B, Cybern., vol. 41, no. 5, pp. 1313-1322, Oct. 2011.
27. E. S. Tognetti, R. C. L. F. Oliveira, and P. L. D. Peres, "Selective H2 and H∞ stabilization of Takagi-Sugeno fuzzy systems, " IEEE Trans. Fuzzy Syst., vol. 19, no. 5, pp. 890-900, Oct. 2011.
28. X. Xie, H. Ma, Y. Zhao, D. Ding, and Y. Wang, "Control synthesis of discrete-time T-S fuzzy systems based on a novel non-PDC control scheme, " IEEE Trans. Fuzzy Syst., vol. 21, no. 1, pp. 147-157, Feb. 2013.
29. X. Xie, D. Yue, and X. Zhu, "Further studies on control synthesis of discrete-time T-S fuzzy systems via useful matrix equalities, " IEEE Trans. Fuzzy Syst., to be published.
30. T. Zou and H. Yu, "Asymptotically necessary and sufficient stability conditions for discrete-time Takagi-Sugeno model: Extended applications of Polya's theorem and homogeneous polynomials, " J. Franklin Inst., vol. 351, no. 2, pp. 922-940, 2014.