Stability Analysis for a Platoon of Vehicles with Reaction-Time Delay

This paper explores collective dynamics in a group of multiple homogeneous vehicles on a ring-road using the Optimal Velocity Model (OVM). To account for real-world traffic scenarios, driver reaction time is incorporated as a time-delay system. Analyzing stability, we initially focus on the equilibrium motion regime, where vehicles maintain uniform speed and spacing. This is achieved through linearization and examining the impact of model parameters. Subsequently, we extend our analysis to the full nonlinear model, determining the equilibrium's region of attraction by solving Linear Matrix Inequalities (LMIs) and estimating ellipsoids.