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Research Papers

Robust Stability and Stabilization of Fractional Order Systems Based on Uncertain Takagi-Sugeno Fuzzy Model With the Fractional Order 1v<2

[+] Author and Article Information
Li Junmin

e-mail: jmli@mail.xidian.edu.cn

Li Yuting

e-mail: yutinglee@126.com
Department of Mathematics,
Xidian University,
Xi'an 710071, PRC

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 20, 2012; final manuscript received January 25, 2013; published online March 26, 2013. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 8(4), 041005 (Mar 26, 2013) (7 pages) Paper No: CND-12-1147; doi: 10.1115/1.4023739 History: Received September 20, 2012; Revised January 25, 2013

This paper addresses the problems of the robust stability and stabilization for fractional order systems based on the uncertain Takagi-Sugeno fuzzy model. A sufficient and necessary condition of asymptotical stability for fractional order uncertain T-S fuzzy model is given, and a parallel distributed compensate fuzzy controller is designed to asymptotically stabilize the model. The results are obtained in terms of linear matrix inequalities. Finally, a numerical example and fractional order Van der Pol system are given to show the effectiveness of our results.

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Figures

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Fig. 1

Time response of the autonomous system in example 1

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Fig. 2

Time response of the closed-loop system states in example 1

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Fig. 3

Control curve of the system in example 1

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Fig. 4

States of Van der Pol system in example 2

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Fig. 5

Control curve of Van der Pol system in example 2

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