Time headway requirements for string stability of homogeneous linear unidirectionally connected systems

This paper investigates string stability issues in homogeneous strings of strictly proper feedback control systems with unidirectional nearest neighbour communications, using only linear systems with two integrators in the loop. We show under which conditions the induced L
₂
-norm of the disturbance to error transfer function is bounded independently of the string length when using a constant time headway and derive a formula for the infimal time headway to guarantee string stability.