[1] Pan JuntaoFei ShuminMu Chaoxu, Xue Mingxiang,. Stabilization design for continuous-time Takagi-Sugeno fuzzy systemsbased on new relaxed conditions [J]. Journal of Southeast University (English Edition), 2010, 26 (4): 550-553. [doi:10.3969/j.issn.1003-7985.2010.04.010]

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Stabilization design for continuous-time Takagi-Sugeno fuzzy systemsbased on new relaxed conditions()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

26

Issue:

2010 4

Page:

550-553

Research Field:

Automation

Publishing date:

2010-12-30

Info

Title:

Stabilization design for continuous-time Takagi-Sugeno fuzzy systemsbased on new relaxed conditions

Author(s):

Pan JuntaoFei ShuminMu Chaoxu;  Xue Mingxiang

Key Laboratory of Measurement and Control of Complex Systems of Engineering ofMinistry of Education, Southeast University, Nanjing 210096, China

Keywords:

Takagi-Sugeno fuzzy model;  fuzzy Lyapunov function;  staircase membership function;  linear matrix inequality

PACS:

TP183

DOI:

10.3969/j.issn.1003-7985.2010.04.010

Abstract:

This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno(T-S)fuzzy systems. New stabilization conditions 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 information of the membership functions can be brought into the stabilization design of the fuzzy systems, thereby significantly reducing the conservativeness in the existing stabilization conditions of the T-S fuzzy systems. Unlike some previous fuzzy Lyapunov function approaches reported in the literature, the proposed stabilization conditions do not depend on the time-derivative of the membership functions that may be the main source of conservatism when considering fuzzy Lyapunov functions analysis. Moreover, conditions for the solvability of the controller design are written in the form of linear matrix inequalities, but not bilinear matrix inequalities, which are easier to be solved by convex optimization techniques. A simulation example is given to demonstrate the validity of the proposed approach.

References:

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[2] Tanaka K, Wang H O. Fuzzy control systems design and analysis: a linear matrix inequality approach [M]. New York, USA:John Wiley and Sons, 2001.
[3] Tanaka K, Hori T, Wang H O. A multiple Lyapunov function approach to stabilization of fuzzy control systems [J]. IEEE Transactions on Fuzzy Systems, 2003, 11(4): 582-589.
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[7] Guerra T M, Vermeiren L. LMI-based relaxed non-quadratic stabilization conditions for nonlinear systems in Takagi-Sugeno’s form [J]. Automatic, 2004, 40(5): 823-829.
[8] Rhee B J, Won S. A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design [J]. Fuzzy Sets and Systems, 2006, 157(9): 1211-1228.
[9] Sala A, Arino C. Relaxed stability and performance LMI conditions for Takagi-Sugeno systems with polynomial constraints on membership function shapes [J]. IEEE Transactions on Fuzzy Systems, 2008, 16(5): 1328-1336.
[10] Lam H K, Narimani M. Quadratic-stability analysis of fuzzy-model-based control systems using staircase membership functions [J]. IEEE Transactions on Fuzzy Systems, 2010, 18(1): 125-137.
[11] Tanaka K, Sugeno M. Stability analysis and design of fuzzy control systems [J]. Fuzzy Sets and Systems, 1992, 45: 135-156.

Memo

Memo:

Biographies: Pan Juntao(1983—), male, graduate; Fei Shumin(corresponding author), male, doctor, professor, smfei@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.60764001, 60835001, 60875035, 61004032), the Postdoctoral Research Fund of Southeast University, the Natural Science Foundation of Jiangsu Province(No.BK2008294).
Citation: Pan Juntao, Fei Shumin, Mu Chaoxu, et al. Stabilization design for continuous-time Takagi-Sugeno fuzzy systems based on new relaxed conditions[J].Journal of Southeast University(English Edition), 2010, 26(4):550-553.

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