Title: Optimizing the Coherence of Composite Networks,
Abstract: We consider how to connect a set of disjoint networks to optimize the
performance of the resulting composite network. We quantify this performance by
the coherence of the composite network, which is defined by an $H_2$ norm of
the system. Two dynamics are considered: noisy consensus dynamics with and
without stubborn agents. For noisy consensus dynamics without stubborn agents,
we derive analytical expressions for the coherence of composite networks in
terms of the coherence of the individual networks and the structure of their
interconnections. We also identify optimal interconnection topologies and give
bounds on coherence for general composite graphs. For noisy consensus dynamics
with stubborn agents, we develop a non-combinatorial algorithm that identifies
connecting edges such that the composite network coherence closely approximates
the performance of the optimal composite graph.