## Title data

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:

**Domains of attraction of interconnected systems : A Zubov method approach.**

*In:*
Proceedings of the European Control Conference (ECC). -
Piscataway, NJ
: IEEE
,
2009
. - pp. 91-96

ISBN 978-3-9524173-9-3

DOI: https://doi.org/10.23919/ECC.2009.7074385

## Related URLs

## Abstract in another language

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: | Article in a book |
---|---|

Refereed: | Yes |

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) |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 19 Feb 2021 09:21 |

Last Modified: | 09 Jan 2024 13:11 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63258 |