Fabio Camilli, Lars Grüne, Fabian Wirth
A regularization of Zubov's equation for robust domains of attraction
Preprint series: Berichte aus der Technomathematik 00-06, Universität Bremen
34D10 Perturbations
49L25 Viscosity solutions
We derive a method for the computation of robust domains of attraction based on a recent generalization of
Zubov's theorem on representing robust domains of attraction for perturbed systems via the viscosity
solution of a suitable partial differential equation. While a direct discretization of the
equation leads to numerical difficulties due to a singularity at the stable equilibrium, a suitable
regularization enables us to apply a standard discretization technique for Hamilton-Jacobi-Bellman
equations. We present the resulting fully discrete scheme and show a numerical example.

Keywords: robust domain of attraction, Zubov's method, viscosity solutions