A generalization of Zubov's method to perturbed systems

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Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
A generalization of Zubov's method to perturbed systems.
Bayreuth , 2002

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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 deterministic perturbations with values in some given compact set of perturbation values. We show that in this general setting a straightforward generalization of the classical Zubov equation has a unique viscosity solution which characterizes the robust domain of attraction as a suitable sublevel set. In addition, we give several properties of this unique viscosity solution (which will not be differentiable in general) and discuss the existence of smooth solutions.