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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.