Analog Data-Driven Theory and Estimation of the Region of Attraction Using Sampled-Data

The contributions of this technical note are twofold. Firstly, we formulate an optimization problem to obtain a linear representation of a nonlinear vector field based on a system's trajectory. We also prove that its cost function is strictly convex, given the trajectory is persistently exciting. Under certain observability conditions, we provide results that guarantee the Hurwitz stability of the global minimizer. Secondly, we present a novel algorithm based on point-wise geometric flows to estimate the boundary of the region of attraction. We show that the algorithm converges to the exact boundary of the region of attraction under certain assumptions on the system dynamics. Finally, we validate the results using simulations on various nonlinear autonomous systems.