Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form

This paper deals with the problem of finite-time stabilization for a class of high-order stochastic nonlinear systems in strict-feedback form. By using Itô’s formula, mathematical induction and backstepping design method, a novel state-feedback controller is constructed to guarantee that the closed-loop high-order nonlinear system has a unique solution and the solution of the closed-loop high-order nonlinear system is finite-time stable. A systematic design algorithm is developed for the construction of the backstepping controller. Finally, the effectiveness of the state-feedback controller is illustrated by two examples.