Analysis of a Class of Hyperbolic Systems via Data-Driven Koopman Operator

The region of attraction of nonlinear dynamical systems is a critical factor in the analysis of equilibrium points. To have an approximation of the region of attraction, we propose the construction and analysis of eigenfunctions coming from the Koopman operator. The construction of eigenfunctions with associated unitary eigenvalue along with the location and local stability of equilibrium points provides a method to find the stable manifolds of saddle points, and in turn, the region of attraction of asymptotically stable points. The method relies on data collected from the trajectories of the underlying system and does not require the knowledge of the differential equation.