Stochastic control for Itô system with state transmission delay

This paper is concerned with the fundamental problem of stochastic control for Itô system with state transmission delay. The optimal controller is firstly given based on the Maximum Principle and the relationship between the state and costate. A sufficient and necessary stabilizing condition is presented for the stochastic system with delayed state. The analytical controller is given in terms of the conditional expectation of the state and the solution to a coupled nonlinear equation developed in this paper.