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This paper aims to design the feedback control based on past states to stabilise a class of nonlinear stochastic differential equations driven by  G -Brownian motion. By building up the connection between the delay feedback control and the control function of no-delay, sufficient conditions are established in terms of size of the time delay ensuring both the  p th moment exponential stability and quasi-surely exponential stability of the delay feedback controlled system. Moreover, methods for determining the upper bound of the length of the time delay and further designing the delay feedback controller are provided. A numerical example is presented to demonstrate our new theory.

Delay feedback stabilisation of stochastic differential equations driven by G -Brownian motion