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Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities

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  • Zhaoxia Duan
  • Zhengrong Xiang
  • Hamid Reza Karimi

Abstract

This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality–based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired controller gains is derived. An illustrative example is provided to show the usefulness and effectiveness of the proposed method.

Suggested Citation

  • Zhaoxia Duan & Zhengrong Xiang & Hamid Reza Karimi, 2014. "Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1402-1415, July.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:7:p:1402-1415
    DOI: 10.1080/00207721.2013.835004
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    References listed on IDEAS

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    1. Guobao Zhang & Ting Wang & Tao Li & Shumin Fei, 2013. "Delay-derivative-dependent stability criterion for neural networks with probabilistic time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(11), pages 2140-2151.
    2. Xiongbo Wan & Huajing Fang, 2013. "Fault detection for discrete-time networked nonlinear systems with incomplete measurements," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(11), pages 2068-2081.
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    Cited by:

    1. Jiang, Yan & Zhai, Junyong, 2019. "Observer-based stabilization of sector-bounded nonlinear stochastic systems in the presence of intermittent measurements," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 740-752.

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