  This paper deals with the problem of string stability of interconnected
systems with double-integrator open loop dynamics (e.g.~acceleration-controlled
vehicles). We analyze an asymmetric bidirectional linear controller, where each
vehicle is coupled solely to its immediate predecessor and to its immediate
follower with different gains in these two directions. We show that in this
setting, unlike with unidirectional or symmetric bidirectional controllers,
string stability can be recovered when disturbances act only on a small
($N$-independent) set of leading vehicles. This improves existing results from
the literature with this assumption. We also indicate that string stability
with respect to arbitrarily distributed disturbances cannot be achieved with
this controller.
