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New approaches to relaxed stabilization conditions and H-infinity control designs for T-S fuzzy systems

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Abstract

This paper focuses on the problem of fuzzy control for a class of continuous-time T-S fuzzy systems. New methods of stabilization design and H-infinity control are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used. Through the staircase membership functions approximating the continuous membership functions of the given fuzzy model, the membership functions can be brought into the design conditions of fuzzy systems, thereby significantly reducing the conservativeness in the recent fuzzy controller design methods. Unlike some previous fuzzy Lyapunov function approaches reported in the literatures, the proposed design techniques of stabilization and H-infinity control do not depend on the time-derivative of the membership functions that may be pointed out as the main source of conservatism when considering fuzzy Lyapunov functions analysis. Moreover, conditions for the solvability of the controller design given here are written in the form of linear matrix inequalities, but not bilinear matrix inequalities, which are easier to be solved by convex optimization techniques. Simulation examples are given to demonstrate the validity and applicability of the proposed approaches.

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Authors and Affiliations

  1. Key Laboratory of Measurement and Control of Complex Systems of Engineering (Ministry of Education), Southeast University, Nanjing Jiangsu, 210096, China

    Juntao Pan, Shumin Fei & Mingxiang Xue

  2. LAMIH, UMR CNRS8503, University of Valenciennes et Hainaut-Cambrésis, Le Mont Houy, 59313, Valenciennes Cedex 9, France

    Juntao Pan

  3. School of Science, Hefei University of Technology, Hefei Anhui, 230009, China

    Yudong Ni

Authors
  1. Juntao Pan
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  2. Shumin Fei
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  3. Yudong Ni
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  4. Mingxiang Xue
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Corresponding author

Correspondence to Juntao Pan.

Additional information

This work was supported by the National Natural Science Foundation of China-Key Program (No. 60835001), and the National Natural Science Foundation of China (No. 61104068).

Juntao PAN received his B.S. and M.S. degrees in Control Theory and Control Engineering from Three Gorges University in 2006 and 2008, respectively. He is currently a Ph.D. candidate at the Research Institute of Automation, Southeast University, Nanjing, China. His current research interests include fuzzy control and nonlinear control.

Shumin FEI received his Ph.D. degree from Beijing University of Aeronautics and Astronautics, China, in 1995. From 1995 to 1997, he was doing postdoctoral research at Research Institute of Automation, Southeast University, China. Currently, he is a professor and doctor advisor at Southeast University. He has published more than 60 journal papers and his research interests include nonlinear systems, and complex systems.

Yudong NI is currently an associate professor at Hefei University of Technology, Hefei, China. His major research fields and topics of interest are nonlinear systems, fuzzy control, and optimal control.

Mingxiang XUE received her B.S. degree in Mathematics Education from Anhui Normal University, and M.S. degree in Applied Mathematics from Anhui University, China in 2002 and 2005, respectively. Currently, she is a Ph.D. candidate in Control Theory and Control Engineering at Southeast University, China. Her research interests include nonlinear systems, and delay systems.

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Pan, J., Fei, S., Ni, Y. et al. New approaches to relaxed stabilization conditions and H-infinity control designs for T-S fuzzy systems. J. Control Theory Appl. 10, 82–91 (2012). https://doi.org/10.1007/s11768-012-0088-9

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  • DOI: https://doi.org/10.1007/s11768-012-0088-9

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