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arXiv · 1810.07927

Generalized Lyapunov criteria on finite-time stability of stochastic nonlinear systems

Xin Yu·Juliang Yin·Suiyang Khoo
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Abstract

This paper considers the problem of finite-time stability for stochastic nonlinear systems. A new Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing results are given, and it shows that this new Lyapunov theorem not only is a generalization of classical stochastic finite-time theorem, but also reveals the important role of white-noise in finite-time stabilizing stochastic systems. In addition, multiple Lyapunov functions-based criteria on stochastic finite-time stability are presented, which further relax the constraint of the infinitesimal generator $\mathcal{L}V$. Some examples are constructed to show significant features of the proposed theorems. Finally, simulation results are presented to demonstrate the theoretical analysis.

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Xin Yu, Juliang Yin, Suiyang Khoo. 2018-10-18. Generalized Lyapunov criteria on finite-time stability of stochastic nonlinear systems. https://doi.org/10.1016/j.automatica.2019.05.048

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