Generalized Lyapunov Criteria on Finite-Time Stability of Stochastic Nonlinear Systems

Abstract

In this talk, I will first introduce established Lyapunov criterion on finite-time stability for stochastic nonlinear systems. Then 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.