  This paper is concerned with the exact controllability of discrete-time
stochastic system which is one of the basic problems of modern control theory.
Though the exact controllability of continuous-time system governed by Ito
stochastic differential equations has been well studied in S. Peng, Progress in
Natural Science, 1994, the counterpart of the discrete-time case is still open
due to the adaptiveness constraint of the controllers and the solvability
challenging of stochastic difference equation with terminal value. The main
contribution in this paper is to present both the Gramian matrix criterion and
the Rank criterion for the exact controllability of discrete-time stochastic
system. The novelty lies in the transformation of the forward stochastic
difference equation into a novel backward one.
