Nonmonotonic observer-based fuzzy controller designs for discrete time T-S fuzzy systems via LMI

IEEE Transactions on Cybernetics

Volumn 44, Issue 12, 2014, Pages 2557-2567

  Derakhshan, Siavash Fakhimi ^a   Fatehi, Alireza ^a   Sharabiany, Mehrad Ghasem ^a  

^a K N TOOSI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Discrete time Takagi Sugeno fuzzy dynamic systems; fuzzy observer; linear matrix inequalities (LMI); nonmonotonic lyapunov function; stabilization

Indexed keywords

CONTROLLERS; DESIGN; DYNAMICAL SYSTEMS; FEEDBACK CONTROL; FUZZY SYSTEMS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; NONLINEAR FEEDBACK; STABILIZATION; STATE FEEDBACK;

DISCRETE-TIME NONLINEAR SYSTEMS; FUZZY OBSERVER; NON QUADRATIC LYAPUNOV FUNCTIONS; NONMONOTONIC; OUTPUT FEEDBACK CONTROLLER; PARALLEL DISTRIBUTED COMPENSATION; TAKAGI SUGENO FUZZY SYSTEMS; TAKAGI-SUGENO;

LINEAR MATRIX INEQUALITIES;

EID: 84912107758     PISSN: 21682267     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCYB.2014.2310591     Document Type: Article

References (39)

1. L. P. Holmblad and J. J. Ostergaard, "Control of a cement kiln by fuzzy logic," Fuzzy Inf. Decision Process., M. M. Gupta and E. Sanchez, Eds. North-Holland 1982, vol. 1, pp. 389-399
2. R. Babuka and H. Verbruggen, "Neuro-fuzzy methods for nonlinear system identification," Annu. Rev. Control, vol. 27, pp. 73-85, Apr. 2003
3. J. C. Bezdek and S. K. Pal, Fuzzy Models for Pattern Recognition: Methods That Search for Structures in Data. New York, NY, USA: IEEE Press, 1992
4. S. K. Pal and S. Mitra, Neuro-Fuzzy Pattern Recognition: Methods in Soft Computing. New York, NY, USA: Wiley, 1999
5. G. Bojadziev and M. Bojadziev, Fuzzy Logic for Business, Finance, and Management. Singapore: World Scientific, 2007
6. R. Draeseke and D. E. A. Giles, "A fuzzy logic approach to modelling the New Zealand underground economy," Math. Comput. Simulation, vol. 59, pp. 115-123, May 2002
7. A. R. Borges and C. H. Antunes, "A fuzzy multiple objective decision support model for energy-economy planning," Eur. J. Oper. Res., vol. 145, pp. 304-316, Mar. 2003
8. L. A. Zadeh, "Fuzzy sets," Inf. control, vol. 8, pp. 338-353, Jun. 1965
9. 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
10. H. Ho, Y. K. Wang, and A. B. Rad, "Robust fuzzy tracking control for robotic manipulators," Simulation Model. Prac. Theory, vol. 15, pp. 801-816, Aug. 2007
11. O. Begovich, E. N. Sanchez, and M. Maldonado, "Takagi-Sugeno fuzzy scheme for real-Yime trajectory tracking of an underactuated robot," IEEE Trans. Control Syst. Technol., vol. 10, no. 1, pp. 14-20, Jan. 2002
12. A. Soukkou, A. Khellaf, S. Leulmi, and K. Boudeghdegh, "Optimal control of a CSTR process," Brazilian J. Chem. Eng., vol. 25, pp. 799-812, Dec. 2008
13. C. Li, J. Zhou, Q. Li, X. An, and X. Xiang, "A new TS fuzzy-modeling approach to identify a boiler-Yurbine system," Expert Syst. Applicat., vol. 37, pp. 2214-2221, Mar. 2010
14. K. Tanaka and M. Sugeno, "Stability analysis and design of fuzzy control systems," Fuzzy Sets Syst., vol. 45, pp. 135-156, Jan. 1992
15. K. Tanaka, T. Ikeda, and H. O. Wang, "Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designs," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 250-265, May 1998
16. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York, NY, USA: Wiley-Interscience, 2001
17. 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
18. M. Johansson, A. Rantzer, and K. E. Arzen, "Piecewise quadratic stability of fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 7, no. 6, pp. 713-722, Dec. 1999
19. G. Feng, "Stability analysis of discrete-Yime fuzzy dynamic systems based on piecewise Lyapunov functions," IEEE Trans. Fuzzy Syst., vol. 12, no. 1, pp. 22-28, Feb. 2004
20. M. De Oliveira, J. Bernussou, and J. C. Geromel, "A new discrete-Yime robust stability condition," Syst. Control Lett., vol. 37, pp. 261-265, Jul. 1999
21. 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
22. C. L. Chen, G. Feng, D. Sun, and X. P. Guan, "H output feedback control of discrete-Yime fuzzy systems with application to chaos control," IEEE Trans. Fuzzy Syst., vol. 13, no. 4, pp. 531-543, Aug. 2005
23. L. Wang and G. Feng, "Piecewise H controller design of discrete time fuzzy systems," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 34, no. 1, pp. 682-686, Feb. 2004
24. D. J. Choi and P. G. Park, "H state-feedback controller design for discrete-Yime fuzzy systems using fuzzy weighting-dependent Lyapunov functions," IEEE Trans. Fuzzy Syst., vol. 11, no. 2, pp. 271-278, Apr. 2003
25. S. Zhou, G. Feng, J. Lam, and S. Xu, "Robust H control for discretetime fuzzy systems via basis-dependent Lyapunov functions," Inf. Sci., vol. 174, pp. 197-217, Aug. 2005
26. T. M. Guerra and W. Perruquetti, "Nonquadratic stabilisation of discrete Takagi-Sugeno fuzzy models," in Proc. 10th IEEE Int. Conf. Fuzzy Syst., 2001, pp. 1271-1274
27. T. M. Guerra and L. Vermeiren, "LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form," Automatica, vol. 40, pp. 823-829, May 2004
28. K. Tanaka, T. Hori, and H. O. Wang, "A multiple Lyapunov function approach to stabilization of fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 11, no. 4, pp. 582-589, Aug. 2003
29. S. F. Derakhshan and A. Fatehi, "Non monotonic Lyapunov functions for stability analysis and stabilization of discrete time Takagi-Sugeno fuzzy systems," Int. J. Innovative Comput. Inf. Control, vol. 10, pp. 1567-1586, Aug. 2014
30. C. Arino, "Relaxed LMI conditions for control of nonlinear Takagi-Sugeno models," Ph.D. dissertation, Dept. Syst., Eng. Control, Polytechnic Univ. Valencia, Valencia, Spain, Dec. 2007
31. L. Xiaodong and Z. Qingling, "New approaches to H controller designs based on fuzzy observers for TS fuzzy systems via LMI," Automatica, vol. 39, pp. 1571-1582, Sep. 2003
32. G. Feng, "A survey on analysis and design of model-based fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 14, no. 5, pp. 676-697, Oct. 2006
33. L. Wang G. Feng, and T. Hesketh, "Piecewise output feedback controller synthesis of discrete time fuzzy systems," in Proc. 42th IEEE Conf. Decision Control, vol. 5. 2003, pp. 4741-4746
34. M. Nachidi, A. Benzaouia, F. Tadeo, and M. A. Rami, "LMIbased approach for output-feedback stabilization for discrete-Yime Takagi-Sugeno systems," IEEE Trans. Fuzzy Syst., vol. 16, no. 5, pp. 1188-1196, Oct. 2008
35. K. Guelton, T. Bouarar, and N. Manamanni, "Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi-Sugeno systems'A descriptor redundancy approach," Fuzzy Sets Syst., vol. 160, pp. 2796-2811, Oct. 2009
36. 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
37. W. J. Wang, Y. J. Chen, and C. H. Sun, "Relaxed stabilization criteria for discrete-Yime T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function," IEEE Trans. Syst, Man, Cybern. B, Cybern., vol. 37, no. 3, pp. 551-559, Jun. 2007
38. A. A. Ahmadi and P. A. Parrilo, "Nonmonotonic Lyapunov functions for stability of discrete time nonlinear and switched systems," in Proc. 47th IEEE Conf. Decision Control, 2008, pp. 614-621
39. L. A. Mozelli and R. M. Palhares, "Less conservative H fuzzy control for discrete-Yime Takagi-Sugeno systems," Math. Prob. Eng., vol. 2011, 2011