  We study platoon control of vehicles with linear third-order longitudinal
dynamics under the constant time headway policy. The controller of each
follower vehicle is only based on its own velocity, acceleration, inter-vehicle
distance and velocity difference with respect to its immediate predecessor,
which are all obtained by on-board sensors. We develop distributed cooperative
extended state observers for followers to estimate the acceleration differences
between adjacent vehicles. Based on estimates of the acceleration differences,
distributed cooperative control laws are designed. By using the stability
theory of perturbed linear systems, we show that the control parameters can be
properly designed to ensure the closed-loop and L2 string stabilities for any
given positive time headway. We further show that the proposed control law
based on the ideal vehicle model can guarantee the closed-loop and L2 string
stabilities even if there are small model parameter uncertainties. Also,
simulation results demonstrate the robustness of the proposed control law
against sensing noises, input delays and parameter uncertainties.
