[1] Liu ShanjianShen Jiong, Liu XichuiLi Yiguo,. Stability analysis for affine fuzzy systembased on fuzzy Lyapunov functions [J]. Journal of Southeast University (English Edition), 2011, 27 (3): 295-299. [doi:10.3969/j.issn.1003-7985.2011.03.014]

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Stability analysis for affine fuzzy systembased on fuzzy Lyapunov functions()

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

Volumn:

27

Issue:

2011 3

Page:

295-299

Research Field:

Automation

Publishing date:

2011-09-30

Info

Title:

Stability analysis for affine fuzzy systembased on fuzzy Lyapunov functions

Author(s):

Liu ShanjianShen Jiong;  Liu XichuiLi Yiguo

School of Energy and Environment, Southeast University, Nanjing 210096, China

Keywords:

affine fuzzy system;  stability analysis;  linear matrix inequalities;  fuzzy Lyapunov function

PACS:

TP183

DOI:

10.3969/j.issn.1003-7985.2011.03.014

Abstract:

An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.

References:

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Memo

Memo:

Biographies: Liu Shanjian(1982—), male, graduate; Shen Jiong(corresponding author), male, doctor, professor, shenj@seu.edu.cn.
Foundation items: Specialized Research Fund for the Doctoral Program of Higher Education(No.20090092110051), the Key Project of Chinese Ministry of Education(No.108060), the National Natural Science Foundation of China(No. 51076027, 51036002, 51106024).
Citation: Liu Shanjian, Shen Jiong, Liu Xichui, et al. Stability analysis for affine fuzzy system based on fuzzy Lyapunov functions[J].Journal of Southeast University(English Edition), 2011, 27(3):295-299.[doi:10.3969/j.issn.1003-7985.2011.03.014]

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