Stability Analysis of the Vehicular Platoon with Sensing Delay and Communication Delay: CTCR Paradigm via Dixon Resultant

For the vehicular platoon consisting of connected automotive vehicles, time delays degrade both the internal stability and string stability. In this study, the internal stability and string stability of the vehicular platoon suffering from sensing delay and communication delay are investigated. In the internal stability analysis, the necessary and sufficient internal stability condition is obtained and the exact time delay margins (ETDMs) are derived via the cluster treatment of characteristic root (CTCR) paradigm. A Dixon resultant matrix-based method is proposed to determine the kernel and offspring hypersurfaces of the CTCR paradigm, and then the computational burden of deriving the ETDMs is reduced significantly. In the string stability analysis, we first propose the string stability conditions for the situation no matter how large the frequency of the leader vehicle's maneuver is. Furthermore, the more practical string stability conditions are studied by considering only the region of low frequency, where most of the energy of the spacing errors exists. Then, a lower bound of the time headway is deduced to enhance road capacity, so the potential of the vehicular platoon is fully motivated. Numerical simulations are provided to illustrate the effectiveness of the theoretical claims.