The paper focuses on spatially distributed control systems where the controller sensing and actuation topology is inherited from that of the plant. Specifically, the paper considers distributed systems composed of linear time-varying subsystems interconnected over general graph structures. These distributed systems are subject to communication latency, where the information sent by a subsystem at the current time step is received by the target subsystem at the next time step. The paper provides convex analysis and synthesis conditions for control design in this setting, with the ℓ2- induced norm used as the performance measure. These conditions reduce to finite sequences of linear matrix inequalities in the case of eventually periodic systems interconnected over finite graphs.