Zubov's method for perturbed differential equations
L. Grüne, F. Camilli, F. Wirth:
Zubov's method for perturbed differential equations
in:
Proceedings of the Mathematical Theory of Networks and Systems (MTNS2000),
CD-Rom, Article B100,
Perpignan,
2000,
Abstract:
We present a generalization of Zubov's method to perturbed differential equations. The goal is to characterize the domain of attraction of a set 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.