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Stable adaptive fuzzy control of nonlinear systems using small-gain theorem and LMI approach
Received:2008/3/11  Revised:2009/1/13
Keywords:Nonlinear control  Fuzzy control  Adaptive control  Small-gain theorem  Input-to-state stability
Fund Project:This work was partly supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No.07KJB510125, 08KJD510008), and the Natural Science Foundation of Yancheng Teachers University (No.07YCKL062, 08YCKL053).
AuthorInstitutionE-mail
Haibo JIANG School of Mathematics, Yancheng Teachers University, Yancheng Jiangsu 224051, China yctcjhb@gmail.com 
Jianjiang YU School of Information Science and Technology, Yancheng Teachers University, Yancheng Jiangsu 224002, China  
Caigen ZHOU School of Information Science and Technology, Yancheng Teachers University, Yancheng Jiangsu 224002, China  
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Abstract:
      A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper. The T-S fuzzy model is employed to represent the systems. First, the concept of the so-called parallel distributed compensation (PDC) and linear matrix inequality (LMI) approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling. Sufficient conditions with respect to decay rate are derived in the sense of Lyapunov asymptotic stability. Finally, the error caused by fuzzy modeling is considered and the input-tostate stable (ISS) method is used to design the adaptive compensation term to reduce the effect of the modeling error. By the small-gain theorem, the resulting closed-loop system is proved to be input-to-state stable. Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded. The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.
Haibo JIANG,Jianjiang YU and Caigen ZHOU.Stable adaptive fuzzy control of nonlinear systems using small-gain theorem and LMI approach[J].Journal of Control Theory and Applications,2010,8(4):527~532.
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