Computation of Time Delay Stability Margin for the Automated Vehicular Platoon

Due to the limited band width and congestion of communication channels in the wireless vehicle-to-vehicle (V2V) communication, time delay inevitably arises and dramatically leads to the disturbances for the automated vehicular platoon. This paper focuses on computing the exact time delay stability margin. In this study, we treat this problem as a stability issue of a consensus system with time delay, where each vehicle in the platoon is recognized as a node, and the interconnected information flow is represented as a graph. Then, the distributed controller is designed by combining the states of the vehicle itself and its neighbouring vehicles. Furthermore, the stability of the entire platoon is analysed according to the characteristic equation of the closed-loop system, and a necessary and sufficient condition for the exact time delay stability margin is obtained. Especially, for the automated vehicular platoon with undirected topology, it is revealed that exact time delay stability margin is determined by the largest eigenvalue of the augmented Laplacian matrix. Furthermore, a rapid method for finding exact time delay stability margin is proposed. Finally, numerical simulations demonstrate that this work generates exact and satisfactory time delay stability margin for the automated vehicular platoon.