Fast finite time stability of stochastic nonlinear systems

This paper focus on fast finite time stability for a class of stochastic nonlinear systems. Firstly, a useful inequality, which will play a crucial role in the fast finite time stability in probability, is expanded on Bihari inequality. Then, the concept of fast finite time stability is discussed for stochastic nonlinear systems and an important theory concerned with fast finite time stability in probability is obtained. Next, a fast finite time state feedback controller can be subtle designed, which not only shortens the convergent time but also requires no large control effort. Three simulation examples are given to support our results of theoretical analysis.