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http://dx.doi.org/10.5391/JKIIS.2003.13.5.582

LMI Based L2 Robust Stability Analysis and Design of Fuzzy Feedback Linearization Control Systems  

Hyun, Chang-Ho (Yonsei University)
Park, Chang-Woo (KETI)
Park, Mignon (Electrical and Computer Department, Yonsei University)
Publication Information
Journal of the Korean Institute of Intelligent Systems / v.13, no.5, 2003 , pp. 582-589 More about this Journal
Abstract
This paper presents the robust stability analysis and design methodology of the fuzzy feedback linearization control systems. Uncertainty and disturbances with known bounds are assumed to be included Un the Takagi-Sugeno (TS) fuzzy models representing the nonlinear plants. $L_2$ robust stability of the closed system is analyzed by casting the systems into the diagonal norm bounded linear differential inclusions (DNLDI) formulation. Based on the linear matrix inequality (LMI) optimization programming, a numerical method for finding the maximum stable ranges of the fuzzy feedback linearization control gains is also proposed. To verify the effectiveness of the proposed scheme, the robust stability analysis and control design examples are given.
Keywords
$L_2$ robust stability; feedback linearization; fuzzy control; linear matrix inequalities; Takagi-Sugeno Fuzzy model;
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1 Kang, H. J., Kwon, C., Lee, C. H. and Park, M. Robust stability analysis and design method for the fuzzy feedback linearization regulator, IEEE Trans. Fuzzy Systems, 1998, 6(4) pp.464-472   DOI   ScienceOn
2 Y.-W. Cho, C.-W. Park, J.-H. Kim and M. Park, "Indirect model reference adaptive fuzzy control of dynamic fuzzy state space model", IEE Proc.-Control Theory Appl., vol. 148, No. 4, July, 2001
3 Fischle, K. and Schroder, D., An improved stable adaptive fuzzy control method, IEEE Trans. Fuzzy Systems, 1999, 7(1) pp.27-40   DOI   ScienceOn
4 Park, C. W., Kang, H. Y., Yee, Y. H. and Park, M., Numerical robust stablity analysis of fuzzy feedback linearization regulator based on linear matrix ineuqality approach, IEE Proc.-Control Theory Appl., in press
5 Takagi, T., Sugeno, M., Fuzzy Identification of systems and its applications to modeling and control, IEEE Trans. Syst., Man, Cybern. 1985, 15(1) pp.116-132
6 Fuh, C. C., Tung, P. C., Robust stability analysis of fuzzy control systems, Fuzzy Sets and Systems, 1997, 88(3) pp.289-298   DOI   ScienceOn
7 Nesterov, Y., Nemirovsky, A., Interior-point polynomial methods in convex programming, SIAM, Philadelphia, 1994
8 Kim, E., Kang, H. J., and Park, M., Numerical stability analysis of fuzzy control systems via quadratic programming and linear matrix inequalities, IEEE Trans. Fuzzy Systems, 1999, 29(4) pp.333-346
9 Vidyasagar, M. Nonlinear system analysis, Prentice-Hall, Englewood Cliffs, 1993
10 Tsay, D. L., Chung, H. Y. and Lee, C. J., The adaptive control of nonlinear systems using the Sugeno-type of fuzzy logic, IEEE Trans. Fuzzy Systems, 1999, 7(2) pp.225-229   DOI   ScienceOn
11 Sugeno, M., Fuzzy control, Nikangoubyou-Shinnbun-sha, Tokyo, 1988
12 Gahinet, P., Nemirovski, A., Laub, A, and Chilali, M., LMI Control Toolbox, The MathWorks, Inc., Natick, 1995
13 Tanaka, K., Ikeda, T., Wang, H. O., Robust stability of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, $H^∞$ control theory, and linear matrix inequalities, IEEE Trans. Fuzzy Systems, 1996, 4(1) pp.1-13   DOI   ScienceOn
14 Boyd, S., Linear matrix inequalities in systems and control theory, SIAM, Philadelphia, 1994
15 Wang, H. O., Tanaka, K., Grifiin, F. G., An approach to fuzzy control of nonlinear system: stability and design issues', IEEE Trans. Fuzzy Systems, 1996, 4(1) pp.14-23   DOI   ScienceOn
16 Kim, E. and Kim D., Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI: discrete case, IEEE Trans. Syst., Man and Cybernetics, 2001, 31(1) pp.132-140   DOI   ScienceOn