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Delay-range-dependent robust stabilisation and control for nonlinear uncertain stochastic fuzzy systems with mode-dependent time delays and Markovian jump parameters

Author

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  • P. Balasubramaniam
  • T. Senthilkumar

Abstract

This article focuses on the problems of robust stabilisation and H∞ control for nonlinear uncertain stochastic systems with mode-dependent time delay and Markovian jump parameters represented by the Takagi–Sugeno (T-S) fuzzy model approach. The system under consideration involves parameter uncertainties, Itô-type stochastic disturbances, Markovian jump parameters and unknown nonlinear disturbances. The purpose is to design a state feedback controller such that the closed-loop system is robustly exponentially stable in the mean square and satisfies a prescribed H∞ performance level. Novel delay-range-dependent conditions in the form of linear matrix inequalities (LMIs) are derived for the solvability of robust stabilisation and H∞ control problem. A desired fuzzy controller can be constructed by solving a set solutions of LMIs and can be easily calculated by Matlab LMI control toolbox. Finally, a numerical example is presented to illustrate the proposed method.

Suggested Citation

  • P. Balasubramaniam & T. Senthilkumar, 2013. "Delay-range-dependent robust stabilisation and control for nonlinear uncertain stochastic fuzzy systems with mode-dependent time delays and Markovian jump parameters," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(1), pages 187-200.
    • Handle: RePEc:taf:tsysxx:v:44:y:2013:i:1:p:187-200
    DOI: 10.1080/00207721.2011.600470
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    Cited by:

    1. R. Rakkiyappan & A. Chandrasekar & S. Lakshmanan, 2016. "Stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2247-2263, July.
    2. Du, Yuanhua & Liu, Xinzhi & Zhong, Shouming, 2016. "Robust reliable H∞ control for neural networks with mixed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 1-8.

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