Computation of the exact time delay margin for vehicle platoon under generic communication topologies

Due to the limited bandwidth and transmission congestion of the vehicle platoon's communication, it is inevitable to induce time delay, which significantly degrades the control performance of the vehicle platoon, even resulting in instability. This paper focuses on analyzing the internal stability under generic communication topologies and presents a method of computing the exact time delay margin (ETDM). The proposed method can offer a necessary and sufficient internal stability condition with no conservatism. Firstly, to reduce the analytical complexity and computational burden elegantly, we decompose the closed-loop platoon dynamics into a set of individual subsystems via similarity transformation and matrix factorization. This decomposition approach is applicable for any general communication topology. Secondly, an explicit formula is deduced to compute the ETDM by surveying the characteristic roots' distribution of all these individual subsystems. It is further demonstrated that only the positive purely imaginary roots need to be considered to compute the ETDM. Finally, simulations are conducted to demonstrate the effectiveness of the theoretical claims.