This paper is concerned with the analysis and synthesis of time-delay interconnected positive systems with external inputs. The interconnected system of interest is constructed from positive subsystems and a nonnegative interconnection matrix, where we assume delays on communications over subsystems. We first analyze the output behavior of the time-delay interconnected positive systems with step and ramp inputs. Then, we second show that the analysis results can be applied to leader-follower-type formation control of moving objects. More precisely, we show a linear-programming-based synthesis condition of the interconnection matrix to achieve a desired formation. We finally demonstrate the effectiveness of the synthesis technique by numerical simulation on time-headway control of a platoon of vehicles.