LMI-based output feedback fuzzy control of chaotic system with uncertainties
Tan Wen(谭文)a), Wang Yao-Nan(王耀南)a), Duan Feng(段峰)a), and Li Xiao-Hui(李晓辉)b)
a College of Electrical and Information Engineering, Hunan University, Changsha 410082, China; b School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
Abstract This paper studies the robust fuzzy control for nonlinear chaotic system in the presence of parametric uncertainties. An uncertain Takagi--Sugeno (T--S) fuzzy model is employed for fuzzy modelling of an unknown chaotic system. A sufficient condition formulated in terms of linear matrix inequality (LMI) for the existence of fuzzy controller is obtained. Then the output feedback fuzzy-model-based regulator derived from the LMI solutions can guarantee the stability of the closed-loop overall fuzzy system. The T--S fuzzy model ofthe chaotic Chen system is developed as an example for illustration. The effectiveness of the proposed controller design methodology is finally demonstrated through computer simulations on the uncertain Chen chaotic system.
Received: 02 July 2005
Revised: 20 January 2006
Accepted manuscript online:
Fund: Project supported by the
National Natural Science Foundation of China (Grant No 60375001), the
Hunan Province Natural\linebreak
\makebox[1.6mm]{}Science Foundation, China (Grant No 03JJY3107) and the
Scientific Research Funds of Hunan Provincial Education
Department,\linebreak
\makebox[1.6mm]{}China (Grant No 05B016).
Cite this article:
Tan Wen(谭文), Wang Yao-Nan(王耀南), Duan Feng(段峰), and Li Xiao-Hui(李晓辉) LMI-based output feedback fuzzy control of chaotic system with uncertainties 2006 Chinese Physics 15 2529
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