Stability analysis and design of Takagi-Sugeno fuzzy systems. (English) Zbl 1097.93023

Summary: This work presents stable composite control criteria for multivariable Takagi-Sugeno (T-S) fuzzy systems. On the basis of the linear matrix inequality (LMI) control strategy and parametric optimization, the composite fuzzy control algorithms are derived. Unlike earlier studies of fuzzy control systems on an LMI framework, this investigation develops a supervisory control approach, such that a fuzzy controller can be synthesized more efficiently. Moreover, a robust control scheme is applied to the T-S fuzzy model with parametric uncertainties. The sufficient conditions are deduced in the form of reduced LMIs and adaptive tuning rules. Finally, numeric simulations are given to validate the proposed approach.


93C42 Fuzzy control/observation systems
Full Text: DOI


[1] Branch, M.A.; Grace, A., Optimization toolbox, (1996), MathWorks Inc. Natick, MA
[2] Cao, S.G.; Rees, N.W.; Feng, G.; Chak, C.K., Design of fuzzy control systems with guaranteed stability, Fuzzy sets syst., 85, 1-10, (1997) · Zbl 0925.93508
[3] Cao, S.G.; Rees, N.W.; Feng, G., H∞ control of uncertain fuzzy continuous-time systems, Fuzzy sets syst., 115, 171-190, (2000) · Zbl 0960.93025
[4] Cheres, E.; Gutman, S.; Palmor, Z.J., Stabilization of uncertain dynamic systems including state delay, IEEE trans. autom. control, 34, 11, 1199-1203, (1989) · Zbl 0693.93059
[5] Cho, Y.W.; Park, C.W.; Park, M., An indirect model reference adaptive fuzzy control for SISO takagi – sugeno model, Fuzzy sets syst., 131, 197-215, (2002) · Zbl 1010.93512
[6] Chang, W.; Park, J.B.; Joo, Y.H.; Chen, G., Design of robust fuzzy-model-based controller with sliding mode control for SISO nonlinear systems, Fuzzy sets syst., 125, 1-22, (2002) · Zbl 1002.93524
[7] Lee, H.J.; Park, J.B.; Chen, G., Robust fuzzy contraol of nonlinear systems with parameter uncertainties, IEEE trans. fuzzy syst., 9, 2, 369-379, (2001)
[8] Liu, X.; Zhang, Q., Approaches to quadratic stability conditions and H∞ control design for T-S fuzzy systems, IEEE trans. fuzzy syst., 11, 6, 830-839, (2003)
[9] Luoh, L., New stability analysis of T-S fuzzy systems with robust approach, Math. comput. simul., 59, 335-340, (2002) · Zbl 1008.93051
[10] Ma, X.J.; Sun, Z.Q.; He, Y.Y., Analysis and design of fuzzy controller and fuzzy observer, IEEE trans. fuzzy syst., 6, 1, 41-51, (1998)
[11] Park, J.; Kim, J.; Park, D., LMI-based design of stabilizing fuzzy controllers for nonlinear systems described by takagi – sugeno fuzzy model, Fuzzy sets syst., 122, 73-82, (2003) · Zbl 0980.93039
[12] Polycarpou, M.M., Stable adaptive neural control scheme for nonlinear systems, IEEE trans. automat. control, 41, 447-451, (1996) · Zbl 0846.93060
[13] Sun, Q.; Li, R.; Zhang, P., Stable and optimal adaptive fuzzy control of complex systems using fuzzy dynamic model, Fuzzy sets syst., 133, 1-17, (2003) · Zbl 1023.93037
[14] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE trans. syst. man cyber., 15, 116-132, (1985) · Zbl 0576.93021
[15] Tanaka, K.; Ikeda, T.; Wang, H.O., Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs, IEEE trans. fuzzy syst., 6, 2, 250-265, (1998)
[16] Tong, S.; Wang, T.; Li, H.X., Fuzzy robust tracking control for uncertain nonlinear systems, Int. J. approx. reason., 30, 73-90, (2002) · Zbl 1008.93050
[17] Tong, S.; Tang, J.; Wang, T., Fuzzy adaptive control of multivariable nonlinear systems, Fuzzy sets syst., 111, 153-167, (2000) · Zbl 0976.93049
[18] Udawatta, L.; Watanabe, K.; Kiguchi, K.; Izumi, K., Fuzzy-chaos controller for controlling of nonlinear systems, IEEE trans. fuzzy syst., 10, 3, 401-411, (2002)
[19] Wang, W.J.; Yan, S.F.; Chiu, C.H., Flexibility stability criteria for a linguistic fuzzy dynamic system, Fuzzy sets syst., 105, 63-80, (1999) · Zbl 0933.93052
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