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[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()
基于模糊Lyapunov函数的仿射模糊模型稳定性分析
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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
基于模糊Lyapunov函数的仿射模糊模型稳定性分析
Author(s):
Liu ShanjianShen Jiong Liu XichuiLi Yiguo
School of Energy and Environment, Southeast University, Nanjing 210096, China
柳善建 沈炯 刘西陲 李益国
东南大学能源与环境学院, 南京 210096
Keywords:
affine fuzzy system stability analysis linear matrix inequalities fuzzy Lyapunov function
仿射模糊模型 稳定性分析 线形矩阵不等式 模糊Lyapunov 函数
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.
研究了基于模糊Lyapunov函数分析连续仿射模糊系统稳定性的方法. 首先, 对模糊系统局部模型的后件部分进行扩展处理, 以便于借鉴齐次模糊模型的稳定性分析方法.然后, 分别得到基于改进公共Lyapunov函数与模糊Lyapunov函数的系统稳定条件, 该条件可表示为一组线性矩阵不等式.通过算例对所得稳定条件进行对比, 结果表明: 基于模糊Lyapunov函数得到的稳定条件与基于改进公共Lyapunov函数的相比具有较小保守性; 对后件部分进行扩展处理后, 尽管稳定性证明方法较简便, 但与不进行后件处理得到的稳定条件相比, 可行解范围有所减小. 最后, 为了增大模糊 Lyapunov 函数的应用范围, 提出了对模糊空间进行划分的方法, 该方法可对隶属度函数为三角形或梯形的模糊系统进行稳定性分析, 得到了基于分段模糊Lyapunov函数的系统稳定条件, 并通过算例验证了所提方法的有效性.

References:

[1] Chang W-J, Huang W-H, Ku C-C. Robust fuzzy control for discrete perturbed time-delay affine Takagi-Sugeno fuzzy models [J]. International Journal of Control, Automation, and Systems, 2011, 9(1): 86-97.
[2] Yeh K, Chen C-Y, Chen C-W. Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method [J]. Applied Mathematics and Computation, 2008, 205(2):568-577.
[3] Jiang X F, Han Q L. Robust H control for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay [J]. IEEE Transactions on Fuzzy Systems, 2007, 15(2):321-331.
[4] Gao R Y, O’Dwyer A. Stability analysis and control synthesis of affine fuzzy systems [C]//The IET China-Ireland International Conference on Information and Communications Technologies. Dublin, Ireland, 2007: 105-112.
[5] Kim E, Kim S. Stability analysis and synthesis for an affine fuzzy control system via LMI and ILMI: continuous case [J]. IEEE Transactions on Fuzzy Systems, 2002, 10(3):391-400.
[6] Kim E, Kim D. Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI: discrete case [J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2001, 31(1): 132-140.
[7] Feng G. Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions[J]. IEEE Transactions on Fuzzy Systems, 2004, 12(1):22-28.
[8] Li Y G, Shen J, Liu X C, et al. ISS controller synthesis of affine fuzzy systems [C]//IEEE International Conference on Control and Automation. Christchurch, New Zealand, 2009:392-397.
[9] Tanaka K, Hori T, Wang H-O. A fuzzy Lyapunov approach to fuzzy control system design [C]//Proceedings of the American Control Conference. Arlington, USA, 2001:4790-4795.
[10] Ji Z C, Zhou Y H, Shen Y X. Stabilization of a class of fuzzy control systems via piecewise fuzzy Lyapunov function approach [C]//Proceedings of the 2007 American Control Conference. New York, USA, 2004:4065-4070.
[11] Johansson M, Rantzer A, Årzén K-E. Piecewise quadratic stability of fuzzy systems [J]. IEEE Transactions on Fuzzy Systems, 1999, 7(6): 713-722.
[12] Tanaka K, Sugeno M. Stability analysis and design of fuzzy control systems [J]. Fuzzy Sets System, 1992, 45(2):135-156.
[13] Tanaka K, Hori T, Wang H O. A dual design problem via multiple Lyapunov functions [C]//IEEE International Fuzzy Systems Conference. Melbourne, Australia, 2001:388-391.
[14] 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, 57(9):1211-1228.
[15] Feng G, Chen C L, Sun D, et al. H controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities [J]. IEEE Transactions on Fuzzy Systems, 2005, 13(1):94-103.
[16] Zhang H B, Li C G, Liao X F. Stability analysis and H controller design of fuzzy large-scale systems based on piecewise Lyapunov functions [J]. IEEE Transactions on Fuzzy Systems, Man, and Cybernetics, Part B: Cybernetics, 2006, 36(3): 685-698.

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]
Last Update: 2011-09-20