Energy-Based Analysis of String Stability in Vehicle Platoons

String stability is a vital property of vehicle platoons which ensures that the system states are not amplified downstream along the string of vehicles. In this paper, a passivity-based approach to stability analysis of vehicle platoons is presented. This is motivated by a case study of an adaptive cruise-controlled platoon. We link the string stability of the platoon to the output strict passivity of each subsystem (vehicle) in the string. We show that a sufficient condition for the platoon to be string stable is that the output strict passivity index of each vehicle in the string be lower bounded by one. For a linear time-invariant (LTI) system, this means the Nyquist plot of the transfer function of each subsystem is within the unit circle. Modeling the platoon as a cascade of LTI subsystems, we present a visual tool to assess string stability. By constraining the output strict passivity index of each subsystem in a string to unity through a two-stage control strategy, the condition for string stability is met. The proposed string stability control strategy, accounting for uncertainties and delays in the drive and sensory systems, is validated using numerical simulations.