Analysis and synthesis of interconnected positive systems with external inputs

In this paper, we deal with an interconnected system constructed from positive subsystems and a nonnegative interconnection matrix. In particular, motivated by leader-follower-type formation control of multi-agent systems, we concentrate our attention on the case where external inputs are applied to the interconnected system. By analyzing the steady-state output of the interconnected system with respect to step and ramp inputs, respectively, we derive synthesis conditions on the interconnection matrix to achieve formation-control-oriented design objectives. We finally illustrate the usefulness of theoretical results via numerical simulation on time-head way control of vehicle platoons.