In this chapter, the problems of stochastic stability, robust stabilization via synchronous state-feedback, and observer-based control are developed for some classes of two-dimensional (2-D) Roesser systems in the presence of state delays and multiplicative stochastic noises. An analysis scheme is first presented and utilized to derive delay-dependent stability conditions in terms of tractable linear matrix inequalities. Applications to the design problem of observer-based control for 2-D systems with exogenous disturbances and random packet dropouts in the control channel is then presented. As some extensions for 2-D systems with multiplicative noises, the stabilization problem via synchronous state-feedback control is also discussed for 2-D Roesser systems driven by inhomogeneous Markov chains. Numerical examples with simulations are given to illustrate the efficacy of the proposed methods.