Stabilisation with general decay rate by delay feedback control for nonlinear neutral stochastic functional differential equations with infinite delay

This paper considers a class of neutral-type stochastic functional differential equations with infinite delay (IDNSFDEs) and highly nonlinear coefficients (i.e., coefficients do not satisfy the linear growth condition). These systems are often unstable. Main aim of this paper is to design a delay feedback control to make them become stable with general decay rate. This general decay stability contains the exponential stability and the polynomial stability. Finally, to illustrate our results more clearly, as examples, this paper also introduces unstable scalar neutral-type stochastic integro-differential equations and discusses their exponential and polynomial stabilisation by delay feedback controls, respectively.