Further Results on T-S Fuzzy Controller Design Subject to Input Constraint
Department of Management Information System, Prefectural University of Hiroshima, 1-1-71 Ujina-higashi, Minami-ku, Hiroshima 734-8558, Japan
In general, when using the Takagi-Sugeno (T-S) fuzzy model to develop a control system, the state feedback control gain can be obtained by solving some linear matrix inequalities (LMIs). In this paper, we consider a class of nonlinear systems with input constraint (saturation). To obtain the control gain, we require to employ certain extra LMIs besides the general ones. As a result, all the LMIs are more conservative. At the same time, one of the extra LMIs confines the initial state to a region, which is referred to as an ellipsoid, and is relevant to a matrix variable in the LMIs. Therefore, the goals of this paper are: 1) making the ellipsoid as large as possible so that the initial state can be confined to the region easily and; 2) making all the LMIs more feasible to obtain the control gain.
-  T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Syst., Man, Cybern., Vol.15, pp. 116-132, 1985.
-  M. Sugeno and G. T. Kang, “Structure identification of fuzzy model,” Fuzzy Sets Syst., Vol.28, No.10, pp. 15-33, 1988.
-  K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control systems,” Fuzzy Sets Syst., Vol.45, No.2, pp. 135-156, 1992.
-  K. Tanaka, T. Ikeda, and H. O. Wang, “Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, H∞ control theory, and linear matrix inequalities,” IEEE Trans. Fuzzy Syst., Vol.4, pp. 1-13, 1996.
-  K. Tanaka and H. O. Wang, “Fuzzy Control System Design and Analysis – A Linear Matrix Inequality Approach,” Wiley, New York, 2001.
-  K. Tanaka, T. Ikeda, and H. O. Wang, “Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based design,” IEEE Trans. Fuzzy Syst., Vol.6, pp. 250-265, 1998.
-  E. Kim and H. Lee, “New approaches to relaxed quadratic stability condition of fuzzy control systems,” IEEE Trans. Fuzzy Syst., Vol.8, No.5, pp. 523-533, 2000.
-  Marcelo C. M. Teixeira, E. Assuncao, and R. G. Avellar, “On relaxed LMI-based designs for fuzzy regulators and fuzzy observers,” IEEE Trans. Fuzzy Syst., Vol.11, No.5, pp. 613-622, 2003.
-  Stanislaw H. Zak, “Stabilizing fuzzy system models using linear controllers,” IEEE Trans. Fuzzy Syst., Vol.7, No.2, pp. 236-240, 1998.
-  X. P. Guan and C. L. Chen, “Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays,” IEEE Trans. Fuzzy Syst., Vol.12, No.2, pp. 236-249, 2004.
-  T. Hu and Z. Lin, “Control Systems with Actuator Saturation: Analysis and Design,” Birkhauser Boston, 2001.
-  T. Hu, Z. Lin, and B. M. Chen, “Analysis and design for a discretetime linear systems subject to actuator saturation,” Syst. Contr. Letter, No.45, pp. 97-112, 2002.
-  T. Hu, Z. Lin, B. Hugang, and Z. Lin, “Absolute stability with a generalized sector condition,” IEEE Trans. Auto. Cont., Vol.49, No.4, pp. 535-548, 2004.
-  Y.-Y Cao and Z. Lin, “Robust stability analysis and fuzzyscheduling control for nonlinear systems subject to actuator saturation,” IEEE Trans. Fuzzy Syst., Vol.11, No.1, pp. 57-67, 2003.
-  Carlos E. de Souza, M. Fu, and L. Xie, “H∞ analysis and synthetic of discrete-times systems with time-varying uncertainty,” IEEE Trans. Auto. Cont., Vol.38, No.3, pp. 459-462, 1993.
-  R. P. Khargonekar, I. R. Pertersen, and K. Zhou, “Robust stabilization of uncertain linear systems: quadratic stabilizability and H∞ control theory,” IEEE Trans. Auto. Cont., Vol.35, No.3, pp. 356-361, 1990.
-  J. S. Thorp and B. R . Barmish, “On guaranteed stability of uncertain linear systems via linear control,” J. Optimiz. Theory Appl., Vol.35, No.4, pp. 559-579, 1981.
-  Hassan K. Khalil, “Nonlinear Systems,” Third edition, Prentice Hall, Upper Saddle River, 2002.
-  P. A. Ioannou and J. Sun, “Robust Adaptive Control,” Prentice Hall PTR, 1996
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.