Practical Asymptotic String Stability in Vehicular Platoons: Controller Design for Enhanced Stability

This paper introduces a new concept of Global Practical Asymptotic String Stability (GPAS) for vehicular platoons subjected to external disturbances. The proposed definition captures the ability of the system to maintain bounded inter-vehicle spacing errors, with convergence bounds that can be adjusted via a tunable control gain. Unlike classical string stability notions based on norms or transfer functions, the GPAS definition explicitly quantifies the trade-off between disturbance attenuation and control gain magnitude. To ensure GPAS, we design a distributed control law based on a backstepping structure, supported by a velocity observer for predecessor estimation. Lyapunov-based analysis establishes local exponential convergence, and sufficient conditions are provided for practical asymptotic string stability. Numerical simulations on a five-vehicle platoon illustrate the effectiveness of the proposed method under idealized conditions.