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We introduce the concept of a control contraction metric, extendingcontraction analysis to constructive nonlinear control design. We derivesufficient conditions for exponential stabilizability of all trajectories of anonlinear control system. The conditions have a simple geometricalinterpretation, can be written as a convex feasibility problem, and areinvariant under coordinate changes. We show that these conditions are necessaryand sufficient for feedback linearizable systems, and also derive novel convexcriteria for exponential stabilization of a nonlinear submanifold of statespace. We illustrate the benefits of convexity by constructing a controller foran unstable polynomial system that combines local optimality and globalstability, using a metric found via sum-of-squares programming.

Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design