  We consider the problem of designing control protocols for nonlinear network
systems affected by heterogeneous, time-varying delays and disturbances. For
these networks, the goal is to reject polynomial disturbances affecting the
agents and to guarantee the fulfilment of some desired network behaviour. To
satisfy these requirements, we propose an integral control design implemented
via a multiplex architecture. We give sufficient conditions for the desired
disturbance rejection and stability properties by leveraging tools from
contraction theory. We illustrate the effectiveness of the results via a
numerical example that involves the control of a multi-terminal high-voltage DC
grid.
