Fabio Camilli, Lars Grüne, Fabian Wirth
Zubov's method for perturbed differential equations.
Preprint series: Proc. MTNS 2000, Perpignan, France
34D10 Perturbations
49L25 Viscosity solutions
We present a generalization of Zubov's method to perturbed differential equations. The goal is to
characterize the domain of attraction of an attractor which is uniformly locally asymptotically stable under all
admissible time varying perturbations. We show that in this general setting the straightforward
generalization of the classical Zubov's equations has a unique viscosity solution which characterizes the
robust domain of attraction as a suitable sublevel set.

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