TAKAGI-SUGENO FUZZY MODELS : AN ILMI APPROACH

This paper deals with the fuzzy based H∞ control problem for time-delay affine Takagi-Sugeno (T-S) fuzzy models. A class of nonlinear time-delay systems is approximated by a time-delay affine T-S fuzzy model in this paper. Based on LyapunovRazumikhin theorem and S-procedure, the stability and stabilization problems are solved by employing a Parallel Distributed Compensation (PDC) type H∞ fuzzy controller. The synthesis for the time-delay affine T-S fuzzy models is a Bilinear Matrix Inequality (BMI) problem and it can not be solved via a convex optimization algorithm. Hence, an Iterative Linear Matrix Inequality (ILMI) algorithm is used to solve the BMI problems in this paper. Finally, a numerical simulation for a delayed pendulum system is given to show the applications of the present approach.

[1]  Kazuo Tanaka,et al.  Fuzzy control systems design and analysis , 2001 .

[2]  W. Chang,et al.  Discrete fuzzy control of time-delay affine takagi-sugeno fuzzy models with H/spl infin/ constraint , 2006 .

[3]  Wen-Jer Chang,et al.  Discrete Fuzzy Controller Design for Achieving Common State Covariance Assignment , 2004 .

[4]  Euntai Kim,et al.  Stability analysis and synthesis for an affine fuzzy control system via LMI and ILMI: a continuous case , 2002, IEEE Trans. Fuzzy Syst..

[5]  Zhang Yi,et al.  Stability of fuzzy control systems with bounded uncertain delays , 2002, IEEE Trans. Fuzzy Syst..

[6]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[7]  Tsu-Tian Lee,et al.  Hybrid compensation control for affine TSK fuzzy control systems , 2004, IEEE Trans. Syst. Man Cybern. Part B.

[8]  Stephen P. Boyd,et al.  Quadratic stabilization and control of piecewise-linear systems , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[9]  M. Malek-Zavarei,et al.  Time-Delay Systems: Analysis, Optimization and Applications , 1987 .

[10]  Euntai Kim,et al.  Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI: discrete case , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[11]  Wen-Jer Chang,et al.  Model-Based Fuzzy Controller Design With Common Observability Gramian Assignment , 2001 .

[12]  Wen-June Wang,et al.  Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Karl-Erik Årzén,et al.  Piecewise quadratic stability of fuzzy systems , 1999, IEEE Trans. Fuzzy Syst..

[14]  Yong-Yan Cao,et al.  Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models , 2001, Fuzzy Sets Syst..

[15]  Jong Hae Kim,et al.  Output feedback robust H∞ control of uncertain fuzzy dynamic systems with time-varying delay , 2000, IEEE Trans. Fuzzy Syst..

[16]  Hua O. Wang,et al.  Fuzzy control of nonlinear time-delay systems: stability and design issues , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[17]  Chein-Chung Sun,et al.  Constrained fuzzy controller design of discrete Takagi-Sugeno fuzzy models , 2003, Fuzzy Sets Syst..

[18]  Wen‐Jer Chang,et al.  Fuzzy covariance control for a class of continuous perturbed nonlinear stochastic systems , 2005 .

[19]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.