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Integral sliding mode control for robust stabilisation of uncertain stochastic time-delay systems driven by fractional Brownian motion

Author

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  • Khosro Khandani
  • Vahid Johari Majd
  • Mahdieh Tahmasebi

Abstract

In this paper, the stability and controller design for fractional stochastic systems, i.e. stochastic systems driven by fractional Brownian motion (fBm) are investigated. A fractional infinitesimal operator is proposed for stability analysis of this class of stochastic systems and a Lyapunov-based stability criterion is established. Thereafter, the presented stability criterion is utilised to develop the sliding mode control scheme for fractional stochastic systems with state delay and time-varying uncertainties. By applying the proposed fractional infinitesimal operator, the sufficient robust stability conditions are derived in the form of linear matrix inequalities. The proposed method guarantees the reachability of the sliding surface in finite time, and the closed-loop system will be stable in probability for all Hurst indices of the fBm in the range (12,1)$({\textstyle{1 \over 2}},1)$. Finally, some simulation examples are given to illustrate the effectiveness of the proposed design method.

Suggested Citation

  • Khosro Khandani & Vahid Johari Majd & Mahdieh Tahmasebi, 2017. "Integral sliding mode control for robust stabilisation of uncertain stochastic time-delay systems driven by fractional Brownian motion," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 828-837, March.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:4:p:828-837
    DOI: 10.1080/00207721.2016.1216201
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    Cited by:

    1. Sweetha, S. & Panneerselvam, V. & Tatar, N. & Sakthivel, R., 2023. "Observer-based control for nonlinear neutral type stochastic model with fractional Gaussian noise and input saturation," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Xu, Xiao & Wang, Li & Du, Zhenbin & Kao, Yonggui, 2023. "H∞ Sampled-Data Control for Uncertain Fuzzy Systems under Markovian Jump and FBm," Applied Mathematics and Computation, Elsevier, vol. 451(C).

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