An output feedback control law is presented, hereafter called the linear quadratic coupled delay compensator (LQCDC), for application to processes that are subjected to randomly varying distributed delays. An example is future generation aircraft, which are equipped with computer networks to serve as the communications link for the vehicle management system. The LQCDC is synthesized via dynamic programming in the stochastic setting. A pair of discrete-time modified matrix Riccati equations and a pair of modified matrix Lyapunov equations are constructed by using lagrangian multipliers and the matrix minimum principle. The performance cost is formulated as the conditional expectation of a quadratic functional adjoined with an equality constraint involving the dynamics of the conditional covariance of the closed-loop system state. Results of simulation experiments are presented to demonstrate the efficacy of the LQCDC for control of longitudinal motion of an advanced aircraft.