## Title data

Grüne, Lars ; Saint-Pierre, Patrick:

**A set valued characterization of ISDS Lyapunov functions.**

*In:*
Proceedings of the 44th IEEE Conference on Decision and Control. -
Piscatawny, NJ, USA
: Institute of Electrical and Electronics Engineers
,
2005
. - pp. 4718-4723

ISBN 0-7803-9567-0

DOI: https://doi.org/10.1109/CDC.2005.1582127

## Abstract in another language

We use set valued analysis techniques in order to characterize Lyapunov functions for the input--to--state dynamical stability (ISDS) property, a quantitatively sharper but qualitatively equivalent variant of the well known input--to--state stability (ISS) property. We show that the epigraphs of minimal ISDS Lyapunov functions are invariance kernels of a suitable augmented differential inclusion. This identity provides theoretical insight into local ISDS properties and yields a basis for a numerical approximation of ISDS and ISS Lyapunov functions via set oriented numerical methods.

## Further data

Item Type: | Article in a book |
---|---|

Refereed: | Yes |

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: | Yes |

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

Date Deposited: | 02 Mar 2021 10:43 |

Last Modified: | 23 Mar 2021 09:13 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63567 |