  We present two sensitivity function trade-offs that apply to a class of
networks with a string topology. In particular we show that a lower bound on
the H-infinity norm and a Bode sensitivity relation hold for an entire family
of sensitivity functions associated with growing the network. The trade-offs we
identify are a direct consequence of growing the network, and can be used to
explain why poorly regulated low frequency behaviours emerge in long vehicle
platoons even when using dynamic feedback.
