  The stability of autonomous vehicle platoons with limits on acceleration and
deceleration is determined. If the leading-vehicle acceleration remains within
the limits, all vehicles in the platoon remain within the limits when the
relative-velocity feedback coefficient is equal to the headway time constant.
Furthermore, if the sensitivity alpha is greater than the relative-velocity
feedback coefficient k, no collisions occur. String stability for small
perturbations is assumed and the initial condition is taken as the equilibrium
state. Other values of k and alpha that give stability with no collisions are
found from simulations. For vehicles with non-negligible mechanical response,
simulations indicate that the acceleration-feedback-control gain might have to
be dynamically adjusted to obtain optimal performance as the response time
changes with engine speed. Stability is demonstrated for some perturbations
that cause initial acceleration or deceleration greater than the limits, yet do
not cause collisions.
