  We consider the problem of controlling a set of dynamically decoupled plants
where the plants' subcontrollers communicate with each other according to a
fixed and known network topology. We assume the communication to be
instantaneous but there is a fixed processing delay associated with incoming
transmissions. We provide explicit closed-form expressions for the optimal
decentralized controller under these communication constraints and using
standard LQG assumptions for the plants and cost function. Although this
problem is convex, it is challenging due to the irrationality of
continuous-time delays and the decentralized information-sharing pattern. We
show that the optimal subcontrollers each have an observer-regulator
architecture containing LTI and FIR blocks and we characterize the signals that
subcontrollers should transmit to each other across the network.
