Global finite-time stabilisation for a class of stochastic high-order time-varying nonlinear systems

In this paper, the problem of global finite-time stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with time-varying nonlinearities. Based on the generalised stochastic Lyapunov theorem on finite-time stability, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed to guarantee that the closed-loop system is globally finite-time stable in probability. Finally, several simulation examples are provided to illustrate the effectiveness of the proposed method.