String stability analysis of homogeneous linear unidirectionally connected systems with nonzero initial conditions

This paper investigates string stability issues in homogeneous strings of strictly proper feedback control systems. We consider initial condition problems with unidirectional nearest neighbour communications, using only linear systems with two integrators in the loop. We define string stability as a type of stability that is uniform with respect to the string length. We show conditions under which the L₂-norm and the L_??-norm of states are bounded and derive a formula for the minimal time headways required to guarantee string stability.