Global stabilisation for a class of stochastic continuous non-linear systems with time-varying delay

This paper studies the problem of global stabilisation for a class of continuous but non-smooth stochastic non-linear systems with time-varying delays. Other than the traditional backstepping recursive control, a concise controller of the nominal system is firstly designed by employing the homogenous domination approach, which overcomes the problem of calculating explosion produced by the diffusion and Hessian terms. Then, by means of an appropriate Lyapunov-Krasoviskii functional and a design parameter, the negative effects of the time delays and non-linear terms generated in the controller design process are dominated; the global asymptotic stability of the closed-loop system can be ensured by the simple but effective controller, which provides significant cost savings. Finally, a simulation example is given to demonstrate the effectiveness of the presented scheme.