Globally asymptotic stabilization of stochastic nonlinear systems in strict-feedback form

Abstract

In this paper, we study the problem of globally asymptotic stabilization for a class of stochastic nonlinear systems. Without requiring the condition that the coefficients are smooth functions, this paper is a first try to apply the backstepping control design method to prove the globally asymptotic stability in probability of stochastic nonlinear systems in strict-feedback form. A continuous control law is constructed by a novel systematic design algorithm. Finally, we provide an example to show the effectiveness of the theoretical results.