Stability analysis of connected vehicles with V2V communication and time delays: CTCR method via Bézout’s resultant

This paper is focused on the distributed control of connected vehicles via vehicle-to-vehicle (V2V) communication. A mixed predecessor following topology with a virtual leader under constant time headway policy is analysed in case of communication and input delays. The longitudinal dynamics of each vehicle in the platoon is represented by a third-order linear model. Unavoidable communication and input delays are introduced into the platoon structure which converts the characteristic equation of the system into a transcendental type. The stability regions of the system in delay space are obtained by utilizing the cluster treatment of characteristic root (CTCR) method in the case of single and multiple time delays. A new Bézout resultant matrix-based approach is proposed to determine the kernel and offspring hypersurfaces of the CTCR method. The determination of these kernel and offspring hypersurfaces becomes computational costly as the number of vehicles increases in the platoon due to the increasing degree of characteristic equation. However, the proposed method reduces the dimensions of the coefficient matrix which is created by using the characteristic equation. It is concluded that the proposed method confirms the internal stability of the connected vehicles with both generic information flow topologies and formation between vehicles under single and multiple time delays. Thereafter, a local string stability definition is proposed in terms of spacing errors. Sufficient conditions to obtain string stability under mixed predecessor following topology for the existence and nonexistence of time delay are given. Finally, several simulation studies with different scenarios are conducted to display the effectiveness of the proposed model and method for internal and string stabilities.