String Stabilization of Predecessor-Following Vehicle Platoons Using Linear Quadratic Integral Control

This paper studies homogeneous vehicle platoons modeled as continuous-time LTI systems under a predecessor-following topology and a constant time-headway spacing policy. The local controller is designed through a Linear Quadratic Integral framework augmented with a double integrator in order to achieve zero steady-state error for ramp-type references. For this setup, we show that internal stability of the local closed loop does not in general imply string stability. We then characterize string stability through the H_∞ norm of the transfer function between consecutive spacing errors and provide a state-space bounded-real Riccati condition based on a reduced-order closed-loop realization. Numerical examples illustrate both string-stable and string-unstable platoons under different choices of time headway and weighting matrices.