Expected String Stability of Human-Led Vehicle Platoons under Stochastic Communication Delays (Full Version)

Abstract

This paper studies expected $\mathcal{L}_2$ string stability of event-triggered vehicle platoons in which a human driver leads a chain of cooperatively controlled autonomous followers under stochastic communication delays. The leader's driving behavior propagates through the string via vehicle-to-vehicle (V2V) communication, so human-induced disturbances must not amplify along the platoon. Unlike deterministic approaches based on worst-case delay bounds, we derive string-stability conditions depending on the full delay distribution through integral inequalities. The closed-loop platoon is modeled as a stochastic hybrid system capturing vehicle dynamics, communication events, and event-triggering. This framework certifies string stability even when delays exceed deterministic admissible bounds with nonzero probability. Results are evaluated under several delay distributions using the MATLAB HyEQ simulator.