  This paper gives convex conditions for synthesis of a distributed control
system for large-scale networked nonlinear dynamic systems. It is shown that
the technique of control contraction metrics (CCMs) can be extended to this
problem by utilizing separable metric structures, resulting in controllers that
only depend on information from local sensors and communications from immediate
neighbours. The conditions given are pointwise linear matrix inequalities, and
are necessary and sufficient for linear positive systems and certain monotone
nonlinear systems. Distributed synthesis methods for systems on chordal graphs
are also proposed based on SDP decompositions. The results are illustrated on a
problem of vehicle platooning with heterogeneous vehicles, and a network of
nonlinear dynamic systems with over 1000 states that is not feedback
linearizable and has an uncontrollable linearization
