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

© 2019 Elsevier Ltd This paper considers the problem of finite-time stability for stochastic nonlinear systems. A general Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing results are also given. This theorem not only generalizes the classical stochastic finite-time theorem, but also somewhat shows that Brownian noise takes an active role in stochastic finite-time stability. In addition, more general conditions on stochastic finite-time stability via multiple Lyapunov functions are given to further relax the constraint of the differential operator LV. Moreover, with the help of this criterion, it shows that an unstable deterministic system can even be finite-time stabilized by Brownian noise. Some concrete examples are constructed to show the significant features of the proposed results, and simulations are presented to verify the theoretical analysis.