## Title data

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

**A generalization of Zubov's method to perturbed systems.**

*In:*
Proceedings of the 41st IEEE Conference on Decision and Control. Volume 3. -
Piscataway, NJ
: IEEE Service Center
,
2002
. - pp. 3518-3523

ISBN 0-7803-7516-5

DOI: https://doi.org/10.1109/CDC.2002.1184420

## Related URLs

## Abstract in another language

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

Refereed: | Yes |

Keywords: | Asymptotic stability; Zubov's method; Robust stability; Domain of attraction; Viscosity solutions |

Institutions of the University: | 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) 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 |

Result of work at the UBT: | No |

DDC Subjects: | 500 Science 500 Science > 510 Mathematics |

Date Deposited: | 01 Mar 2021 13:47 |

Last Modified: | 12 May 2021 05:55 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63398 |