  This paper proposes model reduction approaches for consensus network systems
based on a given clustering of the underlying graph. Namely, given a consensus
network system of time-scaled agents evolving over a weighted undirected graph
and a graph clustering, a parameterized reduced consensus network system is
constructed with its edge weights and nodal time-scales as the parameters to be
optimized. H-infinity- and H-2-based optimization approaches are proposed to
select the reduced network parameters such that the corresponding approximation
errors, i.e., the H-infinity- and H-2-norms of the error system, are minimized.
The effectiveness of the proposed model reduction methods is illustrated via a
numerical example.
