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Robust stability of uncertain T–S fuzzy time-varying systems

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  • Sun, Yeong-Jeu

Abstract

In this paper, the global exponential stability for a class of uncertain Takagi–Sugeno (T–S) fuzzy time-varying systems is investigated. Based on the comparison theorem, a simple criterion is derived to guarantee the global exponential stability of such systems. An estimate of the exponential decay rate of such stable systems is also presented. Finally, a numerical example is provided to illustrate the use of the main result.

Suggested Citation

  • Sun, Yeong-Jeu, 2009. "Robust stability of uncertain T–S fuzzy time-varying systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1588-1594.
  • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1588-1594
    DOI: 10.1016/j.chaos.2007.06.042
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    References listed on IDEAS

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    1. Alimohammady, M. & Roohi, M., 2006. "Fuzzy minimal structure and fuzzy minimal vector spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 599-605.
    2. Huang, Tingwen, 2007. "Exponential stability of delayed fuzzy cellular neural networks with diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 658-664.
    3. Stefanini, Luciano & Sorini, Laerte & Guerra, Maria Letizia, 2006. "Simulation of fuzzy dynamical systems using the LU-representation of fuzzy numbers," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 638-652.
    4. Liu, Xingwen & Zhang, Hongbin & Zhang, Fengli, 2005. "Delay-dependent stability of uncertain fuzzy large-scale systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 147-158.
    5. Feng, Yuhu & Hu, Liangjian, 2006. "On the quasi-controllability of continuous-time dynamic fuzzy control systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 177-188.
    6. Wang, Jiang & Qiao, Guo-Dong & Deng, Bin, 2005. "Observer-based robust adaptive variable universe fuzzy control for chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 1013-1032.
    7. Liu, Xingwen & Zhang, Hongbin, 2005. "Stability analysis of uncertain fuzzy large-scale system," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1107-1122.
    8. Zhang, Hongbin & Yu, Juebang, 2005. "LMI-based stability analysis of fuzzy large-scale systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1193-1207.
    9. Lien, Chang-Hua, 2006. "Further results on delay-dependent robust stability of uncertain fuzzy systems with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 422-427.
    10. Lin, Chong & Wang, Qing-Guo & Lee, Tong Heng, 2006. "Less conservative stability conditions for fuzzy large-scale systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1147-1154.
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