Scaling of H-infinity Norm in Symmetric Bidirectional Platoons*

In this paper scaling of H-infinity norm of selected transfer functions in bidirectional vehicle platoons is investigated. The vehicles are identical and use symmetric nearest-neighbor interactions, hence the communication topology is a pinned undirected path graph. The LTI open-loop model of individual vehicles can be of arbitrary order, but it is required to contain two integrators in order to track the movement of the leader. It is shown that for any agent model some transfer functions in the formation scale linearly, while others scale quadratically. The type of scaling depends on the steady-state gain of the transfer function.