Internal Stability and String Stability of Connected Vehicle Systems With Time Delays

The leader-following consensus method is studied in the connected vehicle systems (CVSs) with the constant time delay. Based on the neighboring vehicle information, the distributed control protocols are designed for the second-order CVSs with the time delay. The necessary and sufficient conditions of internal stability are derived, in which the relationship between the controller parameters and eigenvalues of the Laplician matrix of the network topology is revealed in absence of time delays. Based on such conditions, the sufficient conditions of internal stability are derived and the resulting thresholds of the controller gains are obtained, which are independent of general network topologies. For the CVSs in the presence of the time delay, the necessary and sufficient conditions of internal stability are also derived and the explicit time-delay upper boundary is also given. The two main results are applied to PLF topology and achieve the corresponding necessary and sufficient conditions of internal stability in both the absence and presence of time-delays cases. Considering influence of perturbations, the conditions of the string stability are further derived under the PLF topology, which can ensure perturbations are not amplified downstream, besides guaranteeing stability of the CVSs. Considering time delays and perturbations simultaneously, furthermore, the conditions of both internal stability and string stability are obtained for the PLF topology. Such conditions only depend on the controller parameters and the network weights. So it is convenient to tune the threshold of the controller parameters and determine the time-delay boundary. Simulations are conducted to validate the theoretical results.