Exponential Mean Square Stabilization for Itô Stochastic Systems with Input Delay

This paper is concerned with the Itô stochastic systems with input delay. The main contribution is to establish the equivalent condition for the mean-square stability of the stochastic systems with input delay. The key tool is a parameterized Riccati-ZXL equation. With the solvability of a parameterized Riccati-ZXL equation, we also present the explicit solution of the infinite-horizon optimization problem under a discounted cost function.