New Condition of Stabilization of Uncertain Continuous Takagi-Sugeno Fuzzy System based on Fuzzy Lyapunov Function

Full Text (PDF, 451KB), PP.19-25

Views: 0 Downloads: 0

Author(s)

Yassine Manai 1,* Mohamed Benrejeb 1

1. LA.R.A. Automatique, National School of Engineer of Tunis, El-Manar University, Tunis, Tunisia

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2012.04.03

Received: 2 Apr. 2011 / Revised: 6 Aug. 2011 / Accepted: 29 Oct. 2011 / Published: 8 Apr. 2012

Index Terms

Takagi-Sugeno fuzzy system, uncertain system, Linear Matrix Inequalities LMIs, Fuzzy Lyapunov Function, Parallel Distributed Compensation PDC

Abstract

This paper deals with the stabilization of Takagi-Sugeno fuzzy models. Using non-quadratic Lyapunov function, new sufficient stabilization criteria with PDC controller are established in terms of Linear Matrix Inequality. Finally, a stabilization condition for uncertain system is given.

Cite This Paper

Yassine Manai, Mohamed Benrejeb, "New Condition of Stabilization of Uncertain Continuous Takagi-Sugeno Fuzzy System based on Fuzzy Lyapunov Function", International Journal of Intelligent Systems and Applications(IJISA), vol.4, no.4, pp.19-25, 2012. DOI:10.5815/ijisa.2012.04.03

Reference

[1]Y.Y. Cao and P.M. Frank, “Stability analysis and synthesis of nonlinear time-delay systems via Takagi–Sugeno fuzzy models”, Fuzzy Sets and systems, Vol. 124 N°2, pp. 213-229, 2001.

[2]C. Lin, Q.G. Wang, T.H. Lee, “Delay-dependent LMI conditions for stability and stabilization of T–S fuzzy systems with bounded time-delay”, Fuzzy Sets and Systems, Vol. 157 N°9, pp. 1229-1247, 2006.

[3]L.A. Mozelli, R.M. Palhares, F.O. Souza, and E.M. Mendes, “Reducing conservativeness in recent stability conditions of TS fuzzy systems,” Automatica, Vol. 45, pp. 1580–1583, 2009.

[4]C. Lin, Q.G. Wang, and T. H. Lee, “Fuzzy Weighting-dependent approach to filter deisgn for Time-delay fuzzy systems”, IEEE Transactions on Signal Processing, Vol. 55 N° 6, 2007.

[5]C. Lin, Q.G. Wang, and T. H. Lee, LMI Approach to Analysis and Control of Takagi–Sugeno Fuzzy Systems with Time Delay, Springer-Verlag, Berlin 2007.

[6]Y.Y. Cao, and P.M. Frank. “Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach”. IEEE Transactions on Fuzzy Systems, 8(2), 200-211, 2000.

[7]K. Tanaka, T. Hori, and H.O. Wang, “A multiple Lyapunov function approach to stabilization of fuzzy control systems,” IEEE Transactions on Fuzzy Systems, Vol. 11 N°4, pp. 582–589, 2003.

[8]K. Tanaka, and H.O. Wang, Fuzzy control systems design and analysis: A linear matrix inequality approach. John Wiley and Sons, 2001.

[9]L.A. Mozelli, R.M. Palhares, F.O. Souza, and E.M. Mendes, “Reducing conservativeness in recent stability conditions of TS fuzzy systems,” Automatica, Vol. 45, pp. 1580–1583, 2009.

[10]T. Takagi, and M. Sugeno, “Fuzzy identification of systems and its application to modeling and control,” IEEE Trans. On System, Man and Cybernetics, vol 15 (1), pp. 116–132, 1985. 

[11]M.A.L. Thathachar, P. Viswanah, “On the Stability of Fuzzy Systems”, IEEE Transactions on Fuzzy Systems, Vol. 5, N°1, pp. 145 – 151, February 1997.

[12]K. Tanaka, T. Hori, and H.O. Wang, “A multiple Lyapunov function approach to stabilization of fuzzy control systems,” IEEE Transactions on Fuzzy Systems, Vol. 11 N°4, pp. 582–589, 2003.

[13]K. Tanaka, and H.O. Wang, Fuzzy control systems design and analysis: A linear matrix inequality approach. John Wiley and Sons, 2001.

[14]L. K. Wong, F.H.F. Leung, P.K.S. Tam, “Stability Design of TS Model Based Fuzzy Systems”, Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, Vol. 1, pp. 83–86, 1997.

[15]C.H. Fang, Y.S. Liu, S.W. Kau, L. Hong, and C.H. Lee, “A New LMI-Based Approach to Relaxed Quadratic Stabilization of T–S Fuzzy Control Systems,” IEEE Transactions on Fuzzy Systems, Vol. 14, N° 3, pp.386–397, June 2006. 

[16]H.O. Wang, K. Tanaka, M. F. Griffin, ”An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues”, IEEE Transactions On Fuzzy Systems, Vol. 4, N°1, February 1996.

[17]Tanaka K., Hori T. and Wang H.O., “A fuzzy Lyapunov approach to fuzzy control system design”, Proc. American Control Conf., Arlington VA, pp. 4790–4795.

[18]C.W. Chen, “Stability conditions of fuzzy systems and its application to structural and mechanical systems”, Advances in Engineering Software, Vol. 37, pp. 624 – 629, 2006.

[19]S. Boyd, L. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, Philadelphia, PA: SIAM, 1994.

[20]Y. Manai, M. Benrejeb, “Stability for Continuous Takagi-Sugeno Fuzzy System based on Fuzzy Lyapunov Function’, Conf. CCCA’11, Hammamet, 2011.