{"title":"State Feedback Controller Design via Takagi- Sugeno Fuzzy Model: LMI Approach","authors":"F. Khaber, K. Zehar, A. Hamzaoui","volume":18,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":836,"pagesEnd":842,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12563","abstract":"
In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.<\/p>\r\n","references":"[1] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia,PA, 1994.\r\n[2] K. Tanaka and H.O. Wang, Fuzzy Control Systems Design and Analysis:\r\nA Linear Matrix Inequality Approach, John Wiley & Sons, 2001.\r\n[3] H.O. Wang, K. Tanaka, and M.F. Griffin, \"An approach to fuzzy\r\ncontrol of nonlinear systems: stability and design issues,\" IEEE Trans. Fuzzy Systems, vol. 4, N\u252c\u25911, pp. 14-23, 1996.\r\n[4] J. Zhao, V. Wertz, and R. Gorez, \"Dynamic Fuzzy state feedback Controller and Its limitations,\" Proc. American Contr. Conf., pp. 121-\r\n126,1996.\r\n[5] K. Tanaka and M. Sugeno, \"Stability analysis and design of fuzzy control systems,\" Fuzzy Sets and Systems, vol. 45, pp. 135 -156, 1992.\r\n[6] Y. Nesterov and A. Nemirovski, Interior Point Polynomial Methods in\r\nConvex Programming: Theory and Applications, SIAM, Philadelphia,PA, 1994.\r\n[7] K. Tanaka, T. Ikeda, and H.O. Wang, \"Fuzzy control system design via\r\nLMIs,\" Proc. American Contr. Conf., vol. 5, pp. 2873 -2877, 1997.\r\n[8] K. Tanaka, T. Ikeda, and H.O. Wang, \"Design of fuzzy control system\r\nbased on relaxed LMI Stability conditions,\" Proc. 35th CDC, pp. 598-603, 1996.\r\n[9] P. Dorato, C.T. Abdallah, and V. Cerone, Linear Quadratic Control:\r\nAn Introduction, PrenticeHall, Englewood Cliffs, NJ, 1995.\r\n[10] K. Tanaka, T. Ikeda, and H.O. Wang, \"Robust stabilization of a class of\r\nuncertain nonlinear systems via fuzzy control: quadratic stabilizability,\r\nH\u221e control theory, and linear matrix inequalities,\" IEEE Trans. Fuzzy\r\nSystems, vol. 4, pp. 1-13, 1996.\r\n[11] P. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, LMI Control\r\nToolbox, The Math Works Inc., 1995.\r\n[12] N. E. Mastorakis, \"Modeling dynamical systems via the Takagi-Sugeno\r\nfuzzy model,\" Proceedings of the 4th WSEAS International Conference\r\non Fuzzy sets and Fuzzy Systems, Udine, Italy, march 25-27, 2004.\r\n[13] F. Khaber, A. Hamzaoui, and K. Zehar, \"LMI Approach for robust fuzzy\r\ncontrol of uncertain nonlinear systems,\" 2nd International Symposium on\r\nHydrocarbons & Chemistry, Algeria, March 21-23, 2004.\r\n[14] C. Scherer, S. Weiland. (2004, November 16). Linear Matrix Inequalities\r\nin Control (Online) Available:\r\nhttp:\/\/www.cs.ele.tue.nl\/sweiland\/lmi.html","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 18, 2008"}