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Some properties of finite-time stable stochastic nonlinear systems

Author

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  • Yin, J.
  • Ding, D.
  • Liu, Z.
  • Khoo, S.

Abstract

In this paper we study some properties of finite-time stable stochastic nonlinear systems. We begin by showing several continuous dependence theorems of solutions on initial values under some conditions on the coefficients of stochastic systems. We then derive some regular properties of its stochastic settling time for a finite-time stable stochastic nonlinear system. We show continuity, positive definiteness and boundedness of the expected stochastic settling time under appropriate conditions. Finally, a Lyapunov function is constructed by making use of the expectation of the stochastic settling time, and the infinitesimal generator of the stochastic system defined on the Lyapunov function is also given, and hence resulting in a converse Lyapunov theorem of finite-time stochastic stability.

Suggested Citation

  • Yin, J. & Ding, D. & Liu, Z. & Khoo, S., 2015. "Some properties of finite-time stable stochastic nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 686-697.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:686-697
    DOI: 10.1016/j.amc.2015.02.088
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    References listed on IDEAS

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    1. Yin, Juliang, 2008. "On solutions of a class of infinite horizon FBSDEs," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2412-2419, October.
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    Cited by:

    1. Zhao, Lin & Jia, Yingmin, 2015. "Finite-time consensus for second-order stochastic multi-agent systems with nonlinear dynamics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 278-290.
    2. Zhang, Jing & Xia, Jianwei & Sun, Wei & Zhuang, Guangming & Wang, Zhen, 2018. "Finite-time tracking control for stochastic nonlinear systems with full state constraints," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 207-220.

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