  Finding separable certificates of stability is important for tractability of
analysis methods for large-scale networked systems. In this paper we consider
the question of when a nonlinear system which is contracting, i.e. all
solutions are exponentially stable, can have that property verified by a
separable metric. Making use of recent results in the theory of positive linear
systems and separable Lyapunov functions, we prove several new results showing
when this is possible, and discuss the application of to nonlinear distributed
control design via convex optimization.
