Stabilization in probability and mean square of controlled stochastic dynamical system with state delay

Although stochastic dynamical systems have received a great deal of attention in terms of stabilization studies, so far there are few works on controlled stochastic dynamical systems with state delay. In this paper, a controlled stochastic dynamical system represented by a stochastic differential equation with state delay is considered. Condition under which the system is exponentially stable in mean square and in probability is examined.