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Stability analysis and controller design of interval type-2 fuzzy systems with time delay

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  • Long Sheng
  • Xiaoyu Ma

Abstract

The type-2 fuzzy models can handle the system uncertainties directly based on the type-2 fuzzy sets. In this paper, the Takagi–Sugeno fuzzy model approach is extended to the stability analysis and controller design for interval type-2 (IT2) fuzzy systems with time-varying delay. Delay-dependent robust stability criteria are developed in terms of linear matrix inequalities by using the improvement technique of free-weighting matrices. Less conservative results are obtained by considering the information contained in the footprint of uncertainty. Finally, two simulation examples are presented to illustrate the effectiveness of the theoretical results. One is provided to show the merits of the proposed method, the other based on the continuous stirred tank reactor model is given to illustrate the design processes of IT2 fuzzy controller for a nonlinear system with parameter uncertainties.

Suggested Citation

  • Long Sheng & Xiaoyu Ma, 2014. "Stability analysis and controller design of interval type-2 fuzzy systems with time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(5), pages 977-993, May.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:5:p:977-993
    DOI: 10.1080/00207721.2012.743056
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    References listed on IDEAS

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    1. Wen-Jer Chang & Yu-Teh Meng & Kuo-Hui Tsai, 2012. "AQM router design for TCP network via input constrained fuzzy control of time-delay affine Takagi–Sugeno fuzzy models," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(12), pages 2297-2313.
    2. Lien, Chang-Hua, 2007. "Stabilization for uncertain Takagi–Sugeno fuzzy systems with time-varying delays and bounded uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 645-652.
    3. Yuan-Ming Liu & I-Kong Fong, 2012. "On the controllability and observability of discrete-time linear time-delay systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(4), pages 610-621.
    4. Dongsheng Du & Bin Jiang & Peng Shi, 2012. "Sensor fault estimation and compensation for time-delay switched systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(4), pages 629-640.
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