Further theoretical justification of the κ-samples variation approach for discrete-time takagi-sugeno fuzzy systems

IEEE Transactions on Fuzzy Systems

Volumn 19, Issue 3, 2011, Pages 594-597

  Lee, Dong Hwan ^a   Park, Jin Bae ^a   Joo, Young Hoon ^b  

^a Yonsei University   (South Korea)

^b Kunsan National University   (South Korea)

Author keywords

Discrete time TakagiSugeno (TS) fuzzy systems; linear matrix inequality (LMI); Lyapunov function; relaxation; stability

Indexed keywords

CLASSICAL APPROACH; DISCRETE-TIME; LYAPUNOV; POSITIVE INTEGERS; RELAXATION; TAKAGI SUGENO FUZZY SYSTEMS;

DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL; FUZZY SYSTEMS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; STABILIZATION;

FUZZY SETS;

EID: 79958014914     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2010.2102039     Document Type: Article

References (12)

1. K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, "A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 911-922, Aug. 2009.
2. V. F.Montagner, R. C. L. F. Oliveira, and P. L. D. Peres, "Convergent LMI relaxations for quadratic stabilizability andH∞ control of Takagi-Sugeno fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 863-873, Aug. 2009.
3. B. Ding, "Stabilization of Takagi-Sugeno model via nonparallel distributed compensation law," IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 188-194, Feb. 2010.
4. H. K. Lam andM. Nariman, "Quadratic-stability analysis of fuzzy-modelbased control systems using staircase membership functions," IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 125-137, Feb. 2010.
5. A. Sala and C. Ariño, "Polynomial fuzzy models for nonlinear control: A taylor series approach," IEEE Trans. Fuzzy Syst., vol. 17, no. 6, pp. 1284- 1295, Dec. 2009.
6. A. Sala, "On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems," Annu. Rev. Control, vol. 33, pp. 48-58, 2009.
7. 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.
8. A. Kruszewski and T. M. Guerra, "New approaches for the stabilization of discrete Takagi-Sugeno fuzzy models," in Proc. IEEE Conf. Decis. Control/Eur. Control Conf., Seville, Spain, 2005, pp. 3255-3260. (Pubitemid 46297472)
9. A. Kruszewski, R. Wang, and T. M. Guerra, "Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models: A new approach," IEEE Trans. Autom. Control, vol. 53, no. 2, pp. 606-611, Mar. 2008. (Pubitemid 351493901)
10. T. M. Guerra, A. Kruszewski, andM. 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.
11. T. M. Guerra, A. Kruszewski, and J. Lauber, "Discrete Takagi-Sugeno models for control: Where are we?" Annu. Rev. Control, vol. 33, pp. 37-47, 2009.
12. R. E. Skelton, T. Iwasaki, and K. Grigoriadis, A Unified Algebraic Approach to Linear Control Design. New York/Bristol, PA: Taylor & Francis, 1998.