Global stabilization of switched stochastic nonlinear systems in strict-feedback form under arbitrary switchings

This paper is concerned with the problem of global stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in strictfeedback form and driven by white noise. By introducing a common Lyapunov function, the common state feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment globally exponentially stable. Two examples are given to show the effectiveness of the proposed method.