## Robust stabilization for continuous Takagi-Sugeno fuzzy system based on observer design.(English)Zbl 1264.93131

Summary: We investigate the influence of a new parallel distributed controller (PDC) on the stabilization region of continuous Takagi-Sugeno ($$T-S$$) fuzzy models. Using a nonquadratic Lyapunov function, a new sufficient stabilization criterion is established in terms of linear matrix inequality. The criterion examines the derivative membership function; an approach to determine state variables is given based on observer design. In addition, a stabilization condition for uncertain system is given. Finally, numeric simulation is given to validate the developed approach.

### MSC:

 93C42 Fuzzy control/observation systems 93D21 Adaptive or robust stabilization 93B07 Observability
Full Text:

### References:

 [1] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man and Cybernetics, vol. 15, no. 1, pp. 116-132, 1985. · Zbl 0576.93021 [2] M. A. L. Thathachar and P. Viswanath, “On the stability of fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 5, no. 1, pp. 145-151, 1997. [3] L. K. Wong, F. H. F. Leung, and P. K. S. Tam, “Stability design of TS model based fuzzy systems,” in Proceedings of the 6th IEEE International Conference on Fussy Systems, pp. 83-86, July 1997. [4] I. Abdelmalek, N. Goléa, and M. L. Hadjili, “A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models,” International Journal of Applied Mathematics and Computer Science, vol. 17, no. 1, pp. 39-51, 2007. · Zbl 1133.93032 [5] 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, no. 3, pp. 386-397, 2006. · Zbl 05452543 [6] H. K. Lam and F. H. Leung, Analysis of Fuzzy Model based Control Systems, Springer, Hong Kong, China, 2011. · Zbl 1220.93002 [7] L. A. Mozelli, R. M. Palhares, F. O. Souza, and E. M. A. M. Mendes, “Reducing conservativeness in recent stability conditions of TS fuzzy systems,” Automatica, vol. 45, no. 6, pp. 1580-1583, 2009. · Zbl 1166.93344 [8] C. Hua and S. X. Ding, “Decentralized networked control system design using TS fuzzy approach,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 1, pp. 9-21, 2012. [9] M. Chadli and T.-M. Guerra, “LMI solution for robust static output feedback control of takagi-sugeno fuzzy models,” IEEE Transactions on Fuzzy Systems. In press. [10] M. Chadli and H. R. Karimi, “Robust observer design for unknown inputs takagi-sugeno models,” IEEE Transactions on Fuzzy Systems. In press. · Zbl 1264.93123 [11] K. Zhang, B. Jiang, and P. Shi, “Fault estimation observer design for discrete-time takagisugeno fuzzy systems based on piecewise lyapunov functions,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 1, pp. 192-200, 2012. [12] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1994. · Zbl 0816.93004 [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. A. Mozelli, R. M. Palhares, and G. S. C. Avellar, “A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems,” Information Sciences, vol. 179, no. 8, pp. 1149-1162, 2009. · Zbl 1156.93355 [15] K. Tanaka, T. Hori, and H. O. Wang, “A fuzzy Lyapunov approach to fuzzy control system design,” in Proceedings of the American Control Conference, pp. 4790-4795, Arlington, Va, USA, June 2001. [16] M. Yassine and B. Mohamed, “Condition of stabilisation for continuous takagi-sugeno fuzzy system based on fuzzy lyapunov function,” International Journal of Control and Automation, vol. 4, no. 3, 2011. [17] M. C. M. Teixeira, E. Assun, and R. G. Avellar, “On relaxed LMI-based designs for fuzzy regulators and fuzzy observers,” IEEE Transactions on Fuzzy Systems, vol. 11, no. 5, pp. 613-623, 2003.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.