Non-monotonic Lyapunov functions for stability analysis and stabilization of discrete time Takagi-Sugeno fuzzy systems

International Journal of Innovative Computing, Information and Control

Volumn 10, Issue 4, 2014, Pages 1567-1586

  Derakhshan, Siavash Fakhimi ^a   Fatehi, Alireza ^a  

^a K N TOOSI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Discrete time Takagi Sugeno fuzzy dynamic systems; Iter ative linear matrix inequalities (ILMI); Linear matrix inequalities (LMI); Non monotonic Lyapunov function; Stability analysis; Stabilization

Indexed keywords

FEEDBACK CONTROL; LINEAR MATRIX INEQUALITIES; STABILIZATION; STATE FEEDBACK;

FUZZY DYNAMIC SYSTEMS; GLOBAL ASYMPTOTIC STABILITY; ITER- ATIVE LINEAR MATRIX INEQUALITIES (ILMI); ITERATIVE LINEAR MATRIX INEQUALITY; STABILITY ANALYSIS; STATE FEEDBACK CONTROL LAW; STATE FEEDBACK CONTROLLER; TAKAGI SUGENO FUZZY SYSTEMS;

LYAPUNOV FUNCTIONS;

EID: 84899785286     PISSN: 13494198     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (44)

1. K. Tanaka and M. Sugeno, Stability analysis and design of fuzzy control system, Fuzzy Sets and Systems, vol.45, no.2, pp.135-156, 1992.
2. H. O. Wang, K. Tanaka and M. F. Griffin, An approach to fuzzy control of nonlinear system: Stability and design issues, IEEE Transactions on Fuzzy Systems, vol.4, no.1, pp.14-23, 1996.
3. ∞ control theory, and linear matrix inequalities, IEEE Transactions on Fuzzy Systems, vol.4, no.1, pp.1-13, 1996.
4. ∞ control for uncertain nonlinear systems via state feedback: An LMI approach, Fuzzy Sets and Systems, vol.120, no.1, pp.123-134, 2001.
5. K. Tanaka, T. Taniguchi and H. O. Wang, Fuzzy control based on quadratic performance function: A linear matrix inequality approach, Proc. of the 37th IEEE Conference on Decision & Control, Tampa, FL, USA, pp.2914-2919, 1998.
6. W.-J. Chang, C.-C. Ku, W. Chang and P.-H. Huang, Passive fuzzy control with relaxed conditions for discrete affine T-S fuzzy systems, International Journal of Innovative Computing, Information and Control, vol.3, no.4, pp.853-871, 2007.
7. M. Wang, B. Chen and S. Tong, Adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown time delays, International Journal of Innovative Computing, Information and Control, vol.4, no.4, pp.829-838, 2008.
8. M. Johansson, A. Rantzer and K. E. Arzen, Piecewise quadratic stability of fuzzy systems, IEEE Transactions on Fuzzy Systems, vol.7, no.6, pp.713-722, 1999.
9. ∞ controller design of discrete time fuzzy systems, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol.34, no.1, pp.682-686, 2004.
10. W. J. Wang and C. S. Sun, Relaxed stability condition for T-S fuzzy discrete system, Proc. of IEEE International Conference on Fuzzy Systems, Honolulu, HI, USA, pp.244-249, 2002.
11. I. Zamani and M. H. Zarif, An approach for stability analysis of T-S fuzzy systems via piecewise quadratic stability, International Journal of Innovative Computing, Information and Control, vol.6, no.9, pp.4041-4054, 2010.
12. D. J. Choi and P. Park, State feedback controller design for discrete time switching fuzzy systems, Proc. of the 41th IEEE Conference on Decision & Control, Las Vegas, NV, USA, pp.191-196, 2002.
13. ∞ control for discrete fuzzy systems via basis-dependent Lyapunov functions, Information Sciences, vol.174, no.3-4, pp.197-217, 2005.
14. M. Chadli, D. Maquin and J. Ragot, Relaxed stability condition for Takagi-Sugeno fuzzy systems, Proc. of IEEE International Conference on Systems, Man, and Cybernetics, Nashville, TN, USA, pp.3514-3519, 2000.
15. T. M. Guerra and W. Perruquetti, Non quadratic stabilization of discrete fuzzy model, Proc. of the 10th IEEE International Conference on Fuzzy Systems, Melbourne, Victoria, Australia, pp.1271-1274, 2001.
16. K. Tanaka, T. Taniguchi and H. O. Wang, A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Transactions on Fuzzy Systems, vol.11, no.4, pp.582-589, 2003.
17. V. S. Denysenko, A. A. Martynyuk and V. I. Slynko, Stability analysis of impulsive Takagi-Sugeno systems, International Journal of Innovative Computing, Information and Control, vol.5, no.10(A), pp.3141-3155, 2009.
18. L. Wang and X. Liu, New relaxed stabilization conditions for fuzzy control systems, International Journal of Innovative Computing, Information and Control, vol.5, no.5, pp.1451-1460, 2009.
19. L. X. Wang and J. M. Mendel, Fuzzy basis functions, universal approximation, and orthogonal least squares learning, IEEE Transactions on Neural Networks, vol.3, no.5, pp.807-814, 1992.
20. Y. Wang, G. Rong and S. Wang, Hybrid fuzzy modeling of chemical processes, Fuzzy Sets and Systems, vol.130, no.2, pp.265-275, 2002.
21. A. Soukkou, A. Khellaf, S. Leulmi and K. Boudeghdegh, Optimal control of a CSTR process, Brazilian Journal of Chemical Engineering, vol.25, no.4, pp.799-812, 2008.
22. C. Li, J. Zhou, Q. Li, X. An and X. Xiang, A new T-S fuzzy modeling approach to identify a boiler-turbine system, Expert Systems with Applications, vol.37, no.3, pp.2214-2221, 2010.
23. C. S. Tseng, B. S. Chen and H. J. Uang, Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model, IEEE Transactions on Fuzzy Systems, vol.9, no.3, pp.381-392, 2001.
24. O. Begovich, E. N. Sanchez and M. Maldonado, Takagi-Sugeno fuzzy scheme for real-time trajectory tracking of an underactuated robot, IEEE Transactions on Control Systems Technology, vol.10, no.1, pp.14-20, 2002.
25. H. F. Ho, Y. K. Wong and A. B. Rad, Robust fuzzy tracking control for robotic manipulators, Simulation Modelling Practice and Theory, vol.15, no.7, pp.801-816, 2007.
26. J. Cao, P. Li and H. Liu, An interval fuzzy controller for vehicle active suspension systems, IEEE Transactions on Intelligent Transportation Systems, vol.11, no.4, pp.885-895, 2010.
27. ∞ controller for networked nonlinear manufacturing process interconnected systems based on T-S fuzzy model, Advanced Materials Research, vol.299-300, pp.844-850, 2011.
28. E. Kim and H. Lee, New approaches to relaxed quadratic stability condition of fuzzy control system, IEEE Transactions on Fuzzy Systems, vol.8, no.5, pp.523-533, 2000.
29. W. J. Wang, Y. J. Chen and C. H. Sun, Relaxed stabilization criteria for discrete time T-S fuzzy control systems based on a switching fuzzy model and piecewise lyapunov function, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol.37, no.3, pp.551-559, 2007.
30. M. C. De Oliveira, J. Bernussou and J. C. Geromel, A new discrete time robust stability condition, Systems & Control Letters, vol.37, no.4, pp.261-265, 1999.
31. C. Arino, Relaxed LMI Conditions for Control of Nonlinear Takagi-Sugeno Models, Ph.D. Thesis, Polytechnic University of Valencia, pp.74-77, 2007.
32. ∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI, Automatica, vol.39, no.9, pp.1571-1582, 2003.
33. A. Butz, Higher order derivatives of Liapunov function, IEEE Transactions on Automatic Control, vol.14, no.1, pp.111-112, 1969.
34. A. A. Ahmadi and P. A. Parrilo, Non-monotonic Lyapunov function for stability of discrete time nonlinear and switched systems, Proc. of the 47th IEEE Conference on Decision & Control, Cancun, Mexico, pp.614-621, 2008.
35. R. W. Gunderson, A comparison lemma for higher order trajectory derivatives, Proc. of the American Mathematical Society, vol.27, no.3, pp.543-548, 1971.
36. J. Daafouz, P. Riedinger and C. Lung, Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach, IEEE Transactions on Automatic Control, vol.47, no.11, pp.1883-1887, 2002.
37. D. Mignone, G. F. Trecate and M. Morari, Stability and stabilization of piecewise affine and hybrid systems: An LMI approach, Proc. of the 39th IEEE Conference on Decision & Control, Sydney, New South Wales, Australia, pp.504-509, 2000.
38. T. Zhang, Control of Nonlinear Industrial Systems: Approximate Model Based Approaches, Ph.D. Thesis, City University of Hong Kong, 2008.
39. S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pennsylvania, 1994.
40. 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, 2001.
41. L. E. Ghaoui, F. Oustry and M. A. Rami, A cone complementarity linearization algorithms for static output feedback and related problems, IEEE Transactions on Automatic Control, vol.42, no.8, pp.1171-1176, 1997.
42. 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, 2006.
43. T. M. Guerra and L. Vermeiren, LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in Takagi-Sugeno's form, Automatica, vol.40, no.5, pp.823-829, 2004.
44. C. T. Pang and S. M. Guu, Sufficient conditions for the stability of linear Takagi-Sugeno free fuzzy systems, IEEE Transactions on Fuzzy Systems, vol.11, no.5, pp.695-701, 2003.