3 papers
math.DS2026
RKHS method for computing Koopman-based Lyapunov functions
François-Grégoire Bierwart, Alexandre Mauroy
The Koopman operator is a powerful approach to global stability analysis of nonlinear systems, which provides a systematic procedure for Lyapunov function design. In this framework…
math.DS2026
Error bounds on analytic Koopman-based Lyapunov functions
François-Grégoire Bierwart, Alexandre Mauroy
The Koopman operator provides an infinite-dimensional linear description of nonlinear dynamical systems that can be leveraged in the context of stability analysis. In particular, L…
math.DS2026
A numerical Koopman-based framework to estimate regions of attraction for general vector fields
François-Grégoire Bierwart, Alexandre Mauroy
In this paper, we develop a comprehensive framework to estimate regions of attraction of equilibria for dynamics associated with general vector fields. This framework combines Koop…