This paper studies synchronization using reduced state information based on output information passed between neighbor nodes. The node states are estimated using cooperative dynamical observers at each node. It is shown how to design cooperative state variable state feedbacks and observers at each node that are dual to each other, in a sense that extends the classical system theory notion of duality to dynamical systems on graphs. It is shown that unbounded consensus regions that guarantee synchronization on arbitrary strongly connected digraphs can be guaranteed by using OPTIMAL CONTROL AND OBSERVER design methods at each node based on Riccati equations. A duality theorem for systems on graphs is presented and it is shown how to design cooperative dynamical regulators that use output feedback for tracking the state of a control or leader node.