  We consider a distributed system with identical agents, constant-spacing
policy and asymmetric bidirectional control, where the asymmetry is due to
different controllers, which we describe by transfer functions. By applying the
wave transfer function approach, it is shown that, if there are two integrators
in the dynamics of agents, then the positional coupling must be symmetric,
otherwise the system is locally string unstable. This finding holds also for a
distributed system with a generalized path-graph interaction topology due to
the local nature of the wave transfer function. The main advantage of the
transfer function approach is that it allows us to analyse the bidirectional
control with an arbitrary complex asymmetry in the controllers, for instance,
the control with symmetric positional but asymmetric velocity couplings.
