A state estimation and state feedback control law has been formulated in a stochastic setting, based on the principles of minimum variance filtering and dynamic programming, for application to processes that are subjected to randomly varying distributed delays. The proposed estimation and control law for delay compensation is formulated on the concept of the Linear Quadratic Gaussian (LQG), hereafter called Extended Linear Quadratic Gaussian (ELQG). Although the certainty equivalence property of LQG does not hold for ELQG in general, the combined state estimation and state feedback approach of ELQG offers a suboptimal solution to control of randomly delayed processes. Specifically, ELQG is applicable to analysis and synthesis of Integrated Communication and Control Systems (ICCS) for vehicle management of future generation aircraft and autonomous vehicles where a computer network is employed for distributed processing and on-line information exchange between diverse control and decision-making functions. Results of simulation experiments are presented to demonstrate the efficacy of the ELQG algorithm for flight control of an advanced aircraft.