Zubov's method for perturbed differential equations

Titelangaben

Grüne, Lars ; Camilli, Fabio ; Wirth, Fabian:
Zubov's method for perturbed differential equations.
In: el Jai, Abdelhaq (Hrsg.): Mathematical Theory of Networks and Systems. - Zielona Gora : Techn. Univ. Press , 2001

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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.