In this paper we prove new connections between two frameworks for analysis and control of
nonlinear systems: the Koopman operator framework and contraction analysis. Each …

We propose a novel operator-theoretic framework to study global stability of nonlinear
systems. Based on the spectral properties of the so-called Koopman operator, our approach …

The global description of a nonlinear system through the linear Koopman operator leads to
an efficient approach to global stability analysis. In the context of stability analysis, not much …

This paper introduces the Koopman Control Family (KCF), a mathematical framework for
modeling general discrete-time nonlinear control systems with the aim of providing a solid …

As an example of fruitful cross-fertilization between mathematics and engineering, nonlinear
control theory has attracted considerable effort driven by the need to understand, predict …

The Koopman framework proposes a linear representation of finite-dimensional nonlinear
systems through a generally infinite-dimensional globally linear embedding. Originally, the …

Data-driven models for nonlinear dynamical systems based on approximating the
underlying Koopman operator or generator have proven to be successful tools for …

In this paper, we provide a systematic approach for the design of stabilizing feedback
controllers for nonlinear control systems using the Koopman operator framework. The …

This paper considers the observability of nonlinear systems from a Koopman operator
theoretic perspective–and in particular–the effect of symmetry on observability. We first …

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 …