A converse Lyapunov theorems for stochastic finite-time stability

摘要

This note studies the problem of stochastic finite-time stability of stochastic nonlinear systems. The stochastic finite-time stability means that systems can reach their equilibria in finite-time with a random meaning. Firstly stochastic settling-time function is presented by some function of system trajectory. Along this its properties are given. Secondly the continuity of settling-time function is analyzed. Lastly Lyapunov and converse Lyapunov theorems are given for stochastic finite-time stability.