String Stability of a Third-order Vehicle Model with Inertial Delay Parameters Under Bilateral Control

In this paper, the string stability of bilateral-control systems consisting of third-order models with inertial time-delay parameters is studied. Unlike the double integral model which is always stable under bilateral control conditions, the stability of the third order model can only be guaranteed under constraints. In this paper, the closed-loop stability of large scale platoon is solved by matrix factorization and converted into the stability analysis of the order of the child nodes, and the closed-loop stability conditions are given. On this basis, the string stability of the platoon of vehicles was further studied. By transforming the system matrix into Toeplitz form, the general solution formula of the system equation is obtained. Combined with contradiction proof and inequality analysis, it is proved that the platoon is always string stable under the condition of closed-loop stability. Finally, the conclusion is verified by computer simulation.