Fuzzy systems and controllers: Lyapunov tools for a regionwise approach

Nonlinear Analysis, Theory, Methods and Applications

Volumn 63, Issue 5-7, 2005, Pages 653-665

  Borne, P ^a   Dieulot, J Y ^a  

^a CNRS   (France)

Author keywords

Fuzzy control; Lyapunov functions; Piecewise affine systems; Stability

Indexed keywords

CONTROL EQUIPMENT; FUNCTIONS; LINGUISTICS; LYAPUNOV METHODS; NONLINEAR CONTROL SYSTEMS; SYSTEM STABILITY;

FUZZY SYSTEM; LYAPUNOV FUNCTIONS; NONLINEAR CONTROLLERS; PIECEWISE AFFINE SYSTEMS;

FUZZY CONTROL;

EID: 28044436091     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.09.015     Document Type: Conference Paper

References (45)

1. P. Borne, J.-P. Richard, Local and Global Stability of Attractors by the Use of Vector Norms, the Lyapunov Functions Method and Applications, J.C Baltzer AG Scient. Pub Co (IMACS), 1990, pp. 53-62.
2. P. Borne, J.-P. Richard, and N.E. Radhy Stability, stabilisation, regulation using vector norms A.J. Fossard D. Normand-Cyrot Nonlinear Systems, vol. 2 1997 Chapman & Hall London
3. P. Borne, J.-P. Richard, and M. Tahiri Estimation of attractive domains for locally stable or unstable systems Syst. Anal. Model. Simul. 7 1990 595 610
4. S. Boyd, L. Ghaoui, E. Feron, and V. Balakrishnan Linear Matrix Inequalities in System and Control Theory 1994 SIAM Philiadelphia PA
5. B. Chen, C. Tseng, and H. Uang Robustness design of nonlinear dynamic systems via fuzzy control IEEE Trans. Fuzzy Syst. 7 5 1999 571 585
6. F. Delmotte, L. Dubois, and P. Borne A general scheme for multi-model controller using trust Math. Comput. Simul. 41 1996 173 186
7. M. De Neyer, and R. Gorez Comments on practical design of nonlinear fuzzy controllers with stability analysis for regulating processes with unknown mathematical models Automatica 32 1996 1613 1614
8. J.-Y. Dieulot Design of stable controllers for Takagi-Sugeno systems with concentric characteristic regions Nonlinear Dyn. Syst. Theory 3 2003 63 73
9. J.-Y. Dieulot, and P. Borne Control of an inverted pendulum with the help of a piecewise affine fuzzy controller Stud. Inf. Control 9 2000 45 52
10. J.-Y. Dieulot, and P. Borne Parameter tuning of stable fuzzy controllers J. Intel. Robotic Syst. 33 2002 301 312
11. J.-Y. Dieulot, A. El Kamel, and P. Borne Study of the stability of fuzzy controllers by an estimation of the attraction regions a vector norm approach Math. Problems Eng. 8 2002 221 231
12. J.Y. Dieulot, S. Hajri, and P. Borne Fuzzy control synthesis with the help of fuzzy algorithms Stud. Inf. Control 5 1 1996 5 13
13. L. Dubois, F. Delmotte, P. Borne, and T. Fukuda Stability analysis of a multiple-model controller for constrained uncertain nonlinear systems Int. J. Control 69 1998 519 538
14. L. Dubois, J.-Y. Dieulot, P. Borne, Use of fuzzy logic in multi-model control, IEEE-SMC International Conference, vol. 1, San Antonio, USA, 1994, pp. 471-474.
15. J.S. Glover, and J. Munighan Designing fuzzy controllers from a variable structure standpoint IEEE Trans. Fuzzy Syst. 5 1997 138 144
16. L.J.T. Gruyitch, P. Borne, and J.-C. Gentina General aggregation of large scale systems by vector Lyapunov functions and by vector norms Int. J. Control 24 1976 529 550
17. L.J.T. Gruyitch, J.P. Richard, P. Borne, and J.-C. Gentina Stability of Domains 2004 Chapman & Hall London
18. K.J. Hunt, and T.A. Johansen Design and analysis of gain-scheduled control using local controller networks Int. J. Control 6 1997 619 651
19. T.A. Johansen Fuzzy model based control stability, robustness and performance issues IEEE Trans. Fuzzy Syst. 2 1994 221 234
20. M. Johansson, and A. Rantzer Computation of piecewise quadratic Lyapunov functions for hybrid systems IEEE Trans. Autom. Control 43 1998 555 559
21. M. Johansson, A. Rantzer, and K.-E. Årzén Piecewise quadratic stability of fuzzy systems IEEE Trans. Fuzzy Syst. 7 1999 713 722
22. E. Kim A new approach of numerical stability analysis of fuzzy control systems IEEE Trans. Fuzzy Syst. 31 2001 107 113
23. E. Kim, H. Kang, and M. Park Numerical stability analysis of fuzzy control systems via quadratic programming and linear matrix inequalities IEEE Trans. Syst. Man Cybernet. A 29 1999 333 346
24. A. Kordon, P.S. Dhurjati, Y.O. Fuentes, B.A. Ogunnaike, An intelligent parallel control system structure for plants with multiple operating regimes, J. Proc. Control (1999) 453-460.
25. K.A. Kosanovich, J.G. Charbonneau, and M.J. Piosovo Operating regime-based controller strategy for multi-product processes J. Proc. Control 7 1997 43 56
26. C.C. Lee Fuzzy logic in control systems fuzzy logic controller I-II IEEE Trans. Syst. Man Cybernet. 20 1990 404 418
27. H. Lee, J. Park, and G. Chen Robust fuzzy control of nonlinear systems with parametric uncertainties IEEE Trans. Fuzzy Syst. 9 2001 369 379
28. K. Lee, E. Jeung, and H. Park Robust fuzzy H ∞ control of uncertain nonlinear systems via state feedback an LMI approach Fuzzy Sets Syst. 120 2001 123 134
29. Y.F. Li, and C.C. Lau Development of fuzzy algorithms for servo systems IEEE Control Syst. Mag. 9 1989 65 72
30. R. Palm Sliding mode fuzzy control IEEE International Conference on Fuzzy Systems, San Diego 1992 519 526
31. S. Pettersson, and B. Lennartson An LMI approach for the stability analysis of nonlinear systems Proceedings of ECC Brussels 1997
32. S. Pettersson, and B. Lennartson Exponential stability analysis of nonlinear systems using LMIs Proceedings of CDC San Diego 1997 199 204
33. S. Pettersson, and B. Lennartson Hybrid system stability and robustness verification using linear matrix inequalities Int. J. Control 75 2002 1335 1355
34. A. Rantzer, and M. Johansson Piecewise linear quadratic optimal control IEEE Trans. Autom. Control 45 2000 629 636
35. D.M. Stipanovic, and D.D. Siljak Stability of polytopic systems via convex M -matrices and parameter-dependent Liapunov functions Nonlinear Anal. 40 2000 589 609
36. M. Sugeno On stability of fuzzy systems expressed by fuzzy rules with singleton consequents IEEE Trans. Fuzzy Syst. 7 1999 201 224
37. T. Takagi, and M. Sugeno Fuzzy identification of systems and its applications to modelling and control IEEE Trans. Syst. Man Cybernet. 15 1985 116 132
38. K. Tanaka, T. Ikeda, and H.O. Wang Robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability, H (Infinity) control theory, and linear matrix inequalities IEEE Trans. Fuzzy Syst. 4 1996 1 13
39. K. Tanaka, T. Ikeda, and H.O. Wang Fuzzy regulators and fuzzy observers relaxed stability conditions and LMI-based designs IEEE Trans. Fuzzy Syst. 6 1998 250 265
40. J.S. Taur, and C.W. Cao Design and analysis of region-wise linear fuzzy controllers IEEE Trans. Syst. Man Cybernet. B 26 1996 201 204
41. S.G. Tzafestas, and G.G. Rigatos A simple robust sliding-mode fuzzy logic controller of the diagonal type J. Intel. Robotic Syst. 26 1999 353 388
42. 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. 4 1996 14 23
43. H. Ying Practical design of nonlinear fuzzy controllers with stability analysis for regulating processes with unknown mathematical models Automatica 30 1994 1185 1195
44. K. Zeng, N.-Y. Zhang, and W.-L. Xu A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators IEEE Trans. Fuzzy Syst. 8 2000 773 780
45. J.-M. Zhang, R.-H. Li, and P.-A. Zhang Stability analysis and systematic design of fuzzy control systems Fuzzy Sets Syst. 120 2001 65 72