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

TL;DR

This paper introduces a new Lyapunov theorem for stochastic finite-time stability, generalizing existing results and highlighting the role of white noise, with multiple criteria and simulations validating the approach.

Contribution

It proposes a generalized Lyapunov theorem for stochastic finite-time stability and develops multiple Lyapunov function criteria that relax previous constraints.

Findings

The new theorem generalizes classical stochastic finite-time stability results.

Multiple Lyapunov criteria provide more flexible stability conditions.

Simulations confirm the effectiveness of the proposed theorems.

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.