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A generalization of Zubov's method to perturbed systems

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005492
URN to cite this document: urn:nbn:de:bvb:703-epub-5492-4

Title data

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.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): Erscheint in: Proceedings of the 41st IEEE Conference on Decision and Control. Volume 3. - Piscataway, NJ : IEEE Service Center , 2002 . - S. 3518-3523; https://doi.org/10.1109/CDC.2002.1184420
Keywords: Asymptotic stability; Zubov's method; Robust stability; Domain of attraction; Viscosity solutions
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5492-4
Date Deposited: 12 May 2021 05:55
Last Modified: 21 Jun 2021 09:24
URI: https://epub.uni-bayreuth.de/id/eprint/5492
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