Contraction metric computation using numerical Integration and quadrature

We present a novel method to compute contraction metrics for general nonlinear dynamical systems with exponentially stable equilibria. Such a contraction metric delivers information on the long term behaviour of the system and is robust with respect to perturbations of the dynamics, even perturbations that shift the equilibrium. We prove that our method is always able to deliver a contraction metric in any compact subset of the basin of attraction of an exponentially stable equilibrium. Further, we demonstrate the applicability of the method by computing contraction metrics for two three-dimensional systems from the literature.