Stabilization of random nonlinear systems with unmodeled dynamics

A class of nonlinear systems described by random differential equations (RDEs) in the presence of unmodeled dynamics are considered in this paper. Under the assumption of unmodeled dynamics having enough stability margin, a feedback stabilization controller is consecutively designed by backstepping method and separation technique. The method of ordinary differential equations is used to analyze the stability of the closed-loop system. It is shown that the closed-loop system is noise-to-state stable in probability (NSS-P) and the system can be stabilized in some sense. Finally, a simulation example is used to illustrate the validity of our results.