Robust fuzzy control of a class of fuzzy bilinear systems with time-delay

Abstract This paper presents robust fuzzy controllers for a class of T–S fuzzy bilinear systems (FBSs) with time-delay. First, we adopt the parallel distributed compensation (PDC) method to design a fuzzy controller to stabilize the T–S FBS with time-delay. The stability conditions of the overall fuzzy control system are formulated by linear matrix inequalities (LMIs). Secondly, we propound some LMI conditions to set up the robust controller to stabilize the uncertain T–S FBS with time-delay. Finally, the validity and applicability of the proposed schemes are demonstrated by simulations.

[1]  Chang-Hua Lien,et al.  Non-fragile guaranteed cost control for uncertain neutral dynamic systems with time-varying delays in state and control input , 2007 .

[2]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[3]  Euntai Kim,et al.  New approaches to relaxed quadratic stability condition of fuzzy control systems , 2000, IEEE Trans. Fuzzy Syst..

[4]  Tzuu-Hseng S. Li,et al.  T–S Fuzzy Bilinear Model and Fuzzy Controller Design for a Class of Nonlinear Systems , 2007, IEEE Transactions on Fuzzy Systems.

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

[6]  Y. Cao,et al.  Robust stabilization of uncertain systems with time-varying multistate delay , 1998, IEEE Trans. Autom. Control..

[7]  Lin-Goei Shiau,et al.  Decentralized stabilization of fuzzy large-scale systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[8]  Ronald R. Mohler,et al.  Natural Bilinear Control Processes , 1970, IEEE Trans. Syst. Sci. Cybern..

[9]  Kiriakos Kiriakidis,et al.  Fuzzy model-based control of complex plants , 1998, IEEE Trans. Fuzzy Syst..

[10]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  Yushun Fan,et al.  A chaos search immune algorithm with its application to neuro-fuzzy controller design , 2006 .

[12]  Yong-Yan Cao,et al.  Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach , 2000, IEEE Trans. Fuzzy Syst..

[13]  B. Cui,et al.  Robust passive control for uncertain discrete-time systems with time-varying delays☆ , 2006 .

[14]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

[15]  Tzuu-Hseng S. Li,et al.  Robust stabilization of a class of singularly perturbed discrete bilinear systems , 2000, IEEE Trans. Autom. Control..

[16]  M. Ikeda,et al.  Stabilization of linear systems with time-varying delay , 1979 .

[17]  Chin-Teng Lin,et al.  Discrete-time optimal fuzzy controller design: global concept approach , 2002, IEEE Trans. Fuzzy Syst..

[18]  Tzuu-Hseng S. Li,et al.  Fuzzy target tracking control of autonomous mobile robots by using infrared sensors , 2004, IEEE Transactions on Fuzzy Systems.

[19]  Jin Bae Park,et al.  Robust fuzzy control of nonlinear systems with parametric uncertainties , 2001, IEEE Trans. Fuzzy Syst..

[20]  Euntai Kim,et al.  Adaptive synchronization of T–S fuzzy chaotic systems with unknown parameters , 2005 .

[21]  Her-Terng Yau,et al.  Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems , 2006 .

[22]  G. Feng,et al.  Quadratic stabilization of uncertain discrete-time fuzzy dynamic systems , 2001 .

[23]  Wei-Yen Wang,et al.  Design of sliding mode controllers for bilinear systems with time varying uncertainties , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[24]  S. Gutman,et al.  Stabilization of uncertain dynamic systems including state delay , 1989 .

[25]  Guanrong Chen,et al.  Adaptive control of discrete-time chaotic systems: a fuzzy control approach , 2004 .

[26]  M. Thoma,et al.  Linear Optimal Control of Bilinear Systems: With Applications To Singular Perturbations And Weak Coupling , 1995 .

[27]  Rami Mangoubi.  Robust Estimation and Failure Detection: A Concise Treatment , 1998 .

[28]  Hak-Keung Lam,et al.  Stable and robust fuzzy control for uncertain nonlinear systems , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[29]  Jenq-Der Chen.  Robust H∞ output dynamic observer-based control of uncertain time-delay systems , 2007 .

[30]  Bor-Sen Chen,et al.  Robustness design of nonlinear dynamic systems via fuzzy linear control , 1999, IEEE Trans. Fuzzy Syst..

[31]  Kazuo Tanaka,et al.  Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs , 1998, IEEE Trans. Fuzzy Syst..

[32]  Chin-Wang Tao,et al.  Robust fuzzy control for a plant with fuzzy linear model , 2005, IEEE Transactions on Fuzzy Systems.

[33]  Kazuo Tanaka,et al.  Stability and stabilizability of fuzzy-neural-linear control systems , 1995, IEEE Trans. Fuzzy Syst..

[34]  C. Lien.  Further results on delay-dependent robust stability of uncertain fuzzy systems with time-varying delay , 2006 .