Présentation sur YouTube.

In this talk, we present new connections between two frameworks for analysis and control of nonlinear systems: the Koopman operator framework and contraction analysis. Each method, in different ways, provides exact and global analyses of nonlinear systems by way of linear systems theory. We show equivalence between contraction and Koopman approaches for a wide class of stability analysis and control design problems. The findings are based on a novel relation between the Koopman method and construction of a Kazantzis-Kravaris-Luenberger observer. These results are also extended to discrete-time systems, based on which we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. A significant merit of the proposed approach is that it allows for unconstrained optimization over the Koopman embedding and operator jointly while enforcing stability of the model, via a direct parameterization of stable linear systems, greatly simplifying the computations involved.