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Domains of attraction of interconnected systems : A Zubov method approach

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005581
URN to cite this document: urn:nbn:de:bvb:703-epub-5581-3

Title data

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
Domains of attraction of interconnected systems : A Zubov method approach.
Bayreuth , 2009

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Abstract

We study feedback interconnections of two nonlinear systems, that are asymptotically stable at a fixed point. It is shown that if the subsystems are input-to-state stable and the corresponding gains satisfy a small gain condition, then estimates for the domain of attraction of the whole system may be obtained by calculating robust Lyapunov functions for the subsystems. The latter task can be solved using available Zubov techniques. In total this approach makes numerical computations feasible, as high cost computations only have to be performed in lower dimensions. This comes at the price, that in general only lower approximations of the domain of attraction are obtained and that the system has to be brought in a form, where a small gain condition holds.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erscheint in:
Proceedings of the European Control Conference (ECC). - Piscataway, New Jersey : IEEE , 2009 . - S. 91-96
DOI: https://doi.org/10.23919/ECC.2009.7074385
DDC Subjects: 500 Science > 500 Natural sciences
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-5581-3
Date Deposited: 20 May 2021 12:31
Last Modified: 09 Jun 2021 08:57
URI: https://epub.uni-bayreuth.de/id/eprint/5581

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