  We consider platoons composed of identical vehicles with an asymmetric
nearest-neighbor interaction. We restrict ourselves to intervehicular coupling
realized with dynamic arbitrary-order onboard controllers such that the
coupling to the immediately preceding vehicle is proportional to the coupling
to the immediately following vehicle. Each vehicle is modeled using a transfer
function and we impose no restriction on the order of the vehicle. The platoon
is described by a transfer function in a convenient product form. We
investigate how the H-infinity norm and the steady-state gain of the platoon
scale with the number of vehicles. We conclude that if the open-loop transfer
function of the vehicle contains two or more integrators and the Fiedler
eigenvalue of the graph Laplacian is uniformly bounded from below, the norm
scales exponentially with the growing distance in the graph. If there is just
one integrator in the open loop, we give a condition under which the norm of
the transfer function is bounded by its steady-state gain - the platoon is
string-stable. Moreover, we argue that in this case it is always possible to
design a controller the predecessor following strategy.
