Generalized Lyapunov criteria on finite-time stability of stochastic nonlinear systems
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 . Some examples are constructed to show significant features of the proposed theorems. Finally, simulation results are presented to demonstrate the theoretical analysis.
Keywords
Cite
@article{arxiv.1810.07927,
title = {Generalized Lyapunov criteria on finite-time stability of stochastic nonlinear systems},
author = {Xin Yu and Juliang Yin and Suiyang Khoo},
journal= {arXiv preprint arXiv:1810.07927},
year = {2019}
}