Some results about stabilization of periodic Takagi-Sugeno models

IEEE International Conference on Fuzzy Systems

Volumn , Issue , 2009, Pages 814-819

  Kerkeni, Hichem ^a   Lauber, Jimmy ^a   Guerra, Thierry Marie ^a  

^a UNIVERSITÉ DE VALENCIENNES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE-TIME MODEL; LYAPUNOV; NON-LINEAR; NONLINEAR PERIODIC SYSTEM; SIMULATION EXAMPLE; STABILITY CONDITION; T S MODELS; T-S FUZZY; TAKAGI-SUGENO; TAKAGI-SUGENO MODELS; TIME-VARYING DELAY;

FUZZY CONTROL; FUZZY SYSTEMS; MODAL ANALYSIS; OBSERVABILITY; SIMULATORS; STABILIZATION;

LINEAR MATRIX INEQUALITIES;

EID: 71249106321     PISSN: 10987584     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FUZZY.2009.5277323     Document Type: Conference Paper

References (24)

1. Chauvin, J., Moulin, P., Corde, G., Petit, N. and Rouchon, P. "Real-time nonlinear individual cylinder Air-Fuel Ratio observer on a Diesel engine test bench." In Proc. of the IFAC World Congress. 2005
2. Gaiani G., Lovera M., Colaneri P., and R. Celi. Discrete-time analysis of HHC schemes for helicopter vibration attenuation. In IFAC Workshop on Periodic Control Systems, Yokohama, Japan, 2004, pp. 69-74.
3. Theron A., Farges C., Peaucelle D. and Arzelier D., "Periodic H2 synthesis for spacecraft in elliptical orbits with atmospheric drag and J2perturbations",proceedings of American Control Conference, New York City, USA, july, 2007.
4. Bittanti S. and Colaneri P.. Invariant representations of discrete-time periodic systems. Automatica, 36, 2000, pp. 1777-1793.
5. T. Takagi, M. Sugeno, "Fuzzy identification of systems and its application to modelling and control," IEEE transactions on System, Man and Cybemetics, volume 15,issue 1, pp.116-132, 1985
6. Taniguchi, K. Tanaka, H.O. Wang. "Model construction, rule reduction and robust compensation for generalized form of Takagi-Sugeno fuzzy systems," IEEE Transactions on Fuzzy Systems, volume 9, issue 4, pp. 525-537, 2001.
7. Boyd, L. El Ghaoui, E. Féron, V. Balakrishnan (1994). Linear matrix inequalities in system and control theory. Studies in Applied Mathematics. Philadelphia, PA: SIAM, June.
8. T.M. Guerra, L. Vermeiren (2004). LMI-based relaxed non-quadratic stabilization conditions for nonlinear systems in Takagi-Sugeno's form. Automatica, 40(5), 823-829.
9. T.M. Guerra, A. Kruszewski (2004). Non-quadratic stabilization condition for uncertain discrete nonlinear models in the Takagi-Sugeno's form. IFAC Workshop Advances in Fuzzy and Neural Control, Oulu, Finland, Sept.
10. M.C. de Oliveira, J. Bernussou and , J.C. Geromel, "A new discretetime robust stability condition," Systems and Control Letters, Volume 37, Number 4, pp. 261-265 ,26 July 1999.
11. M. Teixeira, E. Assunçao, R. Avellar (2003). On relaxed LMI- based design for fuzzy regulators and fuzzy observers. IEEE Trans. on Fuzzy Systems, vol 11, no 5, 613-623
12. ∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica, 39(9), 1571-1582 Y.Y. Cao, P.M.
13. H.D. Tuan, P. Apkarian, T. Narikiyo, and Y. Yamamoto. Parameterized linear matrix inequality techniques in fuzzy control system design. IEEE Trans. Fuzzy Systems, 9(2):324-332, 2001.
14. A. Sala, C. Ariño, Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem, Fuzzy Sets and Systems, Volume 158, Issue 24, 16 December 2007, pp. 2671-2686.
15. Farkas, M. (1994). Periodic motions. New York: Springer-Verlag
16. C. Farges, D. Peaucelle, D. Arzelier, and J. Daafouz.," Robust 2 H performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs," Systems & Control Letters, 56 : 159-166, 2007.
17. C.E. de Souza and A. Trofino, "An LMI approach to stabilization of linear discrete-time periodic systems." International Journal of Control, volume 73, issue 8, pages 696-703, 2000.
18. A. Butcher, H. Ma, E. Bueler, V. Averina, and Z. Szabo, Stability of linear time periodic delay-differential equations via Chebyshev polynomials, Internat. J. Numer. Methods Engrg., 59 (2004), pp. 895-922.
19. Stepan, G., Insperger,T., "Stability of time-periodic and delayed systems - a route to actand-wait control", Annual Reviews in Control, 30, pp. 159-168, 2006.
20. Kruszewski A., Guerra T-M. (2007). Stabilization of a class of nonlinear model with periodic parameters in the Takagi-Sugeno form. 3th IFAC Workshop PSYCO'07 (Periodic Control Systems), Saint-Petersburg,Russia,août
21. Y.Y. Cao, P.M. Frank (2001). Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models. Fuzzy Sets & Systems, 124, 213-229.
22. S. Zhou and T. Li, "Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent Lyapunov-Krasovskii function," Fuzzy Sets and Systems, volume 151, pp. 139-153, 2005.
23. S. Xu, T. Chen (2004), Robust H?Dagger; control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers. Systems & Control letters, 51, 171-183.
24. P. Bolzern and P. Colaneri, "The periodic Lyapunov equation," SIAM Journal on Matrix Analysis and Applications, volume 9,issue 4, pp 499-512,October 1988.