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Global state feedback stabilisation of stochastic high-order nonlinear systems with high-order and low-order nonlinearities

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  • Fangzheng Gao
  • Yuqiang Wu
  • Xin Yu

Abstract

In this paper, the problem of global stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with both high-order and low-order nonlinearities, to which the existing control methods are inapplicable. Based on the generalised stochastic Lyapunov theorem, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed, which can guarantee the global asymptotic stability in probability of the resulting closed-loop system in the sense of weak solution, and also is able to lead to an interesting result of finite-time stabilisation under appropriate conditions. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.

Suggested Citation

  • Fangzheng Gao & Yuqiang Wu & Xin Yu, 2016. "Global state feedback stabilisation of stochastic high-order nonlinear systems with high-order and low-order nonlinearities," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(16), pages 3846-3856, December.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:16:p:3846-3856
    DOI: 10.1080/00207721.2015.1129678
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    Cited by:

    1. Liang Liu & Yifan Zhang, 2017. "Decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 838-848, March.
    2. Fangzheng Gao & Yuqiang Wu, 2017. "Finite-time output feedback stabilisation for a class of feedforward nonlinear systems with input saturation," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(6), pages 1254-1265, April.
    3. Chen, Wenbin & Gao, Fang & She, Jinhua & Xia, Weifeng, 2020. "Further results on delay-dependent stability for neutral singular systems via state decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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