My paper with Jean-Jacques Slotine introducing control contraction metrics has just been published in IEEE Transactions on Automatic Control
The main result of this paper is that difficult problems in nonlinear control design can be made easier by thinking about them in terms of differential (local) dynamics and contraction metrics. Roughly speaking, local stabilizability of all trajectories implies global stabilizability of all trajectories.
The search for a metric that verifies this fact can be written as a convex optimization problem, very similar to well-known formulations for linear control design. In particular, problems with polynomial dynamics can easily be solved using sum-of-squares, e.g. via Yalmip