Fabio Camilli, Lars Grüne, Fabian Wirth
A generalization of Zubov's method to perturbed systems
Preprint series: DFG-Schwerpunkt DANSE 24/99
34D10 Perturbations
49L25 Viscosity solutions
A generalization of Zubov's theorem on representing the domain of attraction via the solution of a suitable
partial differential equation is presented for the case of perturbed systems with a singular fixed point. For
the construction it is necessary to consider solutions in the viscosity sense. As a consequence maximal robust
Lyapunov functions can be characterized as viscosity solutions.

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