Finite-time stabilization of weak solutions for a class of non-local Lipschitzian stochastic nonlinear systems with inverse dynamics

In this paper, finite-time stabilization is investigated for a class of non-local Lipschitzian stochastic nonlinear systems with stochastic inverse dynamics. Different from the existing work about finite-time control, to guarantee the existence of the solution under mild conditions, we study the stabilization in the sense of weak solution. We first present a finite-time stability theory under the framework of weak solution. Then, for a class of stochastic nonlinear systems with stochastic inverse dynamics, a finite-time controller via state feedback is constructively designed under the assumption that the stochastic inverse dynamics is stochastic input-to-state stable. The trivial weak solution of the closed-loop system is proved to be globally finite-time stable in probability. Finally, a simulation example is given to illustrate the efficiency of the proposed design procedure.