Design and Analysis of Longitudinal Controller for the Platoon With Time-Varying Delay

The communication topologies between vehicles in a platoon substantially impact the platoon's stability. This study provides a distributed linear feedback control law that considers time-varying delay with guaranteed internal and string stability of the platoon system under various communication topologies. Firstly, the vehicle dynamics linearized model was derived using the precise feedback linearization technology. Different types of communication topologies, such as vehicle-to-vehicle communication and sensor-based communication, were described using directed graphs. Secondly, the linear feedback control law was designed to establish the stable zone of the linear controller gain under the effect of different communication topologies using directed graphs and the Routh-Hurwitz stability theorem. The Lyapunov-Razumikhin theorem determines the upper bound of the time-varying delay of various communication topologies. Additionally, the string stability of leader-predecessor following topology was studied, and the results were combined with the internal stability to determine the upper bound of time-varying delay. Finally, the results were verified by conducting two numerical simulations.