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,

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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.

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