Controllability of Stochastic Integro-Differential Systems with Time Delay in Control Input

This paper investigates the relative controllability problem of semilinear stochastic integro-differential systems with a variable delay in control. Under suitable conditions, it is shown that the semilinear stochastic system may be steered up to the reachable set of its corresponding linear system in finite terminal time. The results are obtained by using fixed point argument. Finally a numerical example is provided to illustrate the technique.