  In this paper, 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. Interestingly, we
prove that every discrete-time nonlinear contracting model can be learnt in our
framework. Another 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. We validate our
method on a simulated system and analyze the advantages of our parameterization
compared to alternatives.
