A multi-variable PI (proportional integrating) controller is proved to be optimal for an
important class of control problems where performance is specified in terms of frequency
weighted H-infinity norms. The problem class includes networked systems with a subsystem
in each node and control action along each edge. For such systems, the optimal PI controller
is decentralized in the sense that control action along a given network edge is entirely
determined by states at nodes connected by that edge.