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This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semilinear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability of fractional dynamical systems.

In this article, we are concerned with the problem of relative controllability for non-linear stochastic systems with distributed delays in control in finite-dimensional spaces. Sufficient criteria for the relative controllability of the non-linear stochastic system are established. Some special cases are also considered. The results are obtained by using the Banach fixed point theorem. An example is provided to illustrate the technique.