## Title data

Grüne, Lars ; Saint-Pierre, Patrick:

**An invariance kernel representation of ISDS Lyapunov functions.**

*In:* Systems & Control Letters.
Vol. 55
(2006)
Issue 9
.
- pp. 736-745.

ISSN 1872-7956

DOI: https://doi.org/10.1016/j.sysconle.2006.02.003

## Related URLs

## Abstract in another language

We apply set valued analysis techniques in order to characterize the input--to--state dynamical stability (ISDS) property, a variant of the well known input--to--state stability (ISS) property. Using a suitable augmented differential inclusion we are able to characterize the epigraphs of minimal ISDS Lyapunov functions as invariance kernels. This characterization gives new insight into local ISDS properties and provides a basis for a numerical approximation of ISDS and ISS Lyapunov functions via set oriented numerical methods.

## Further data

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

Refereed: | Yes |

Keywords: | Input-to-state stability; Invariance kernel; Lyapunov functions; Set valued analysis; Set oriented numerics |

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 12:20 |

Last Modified: | 09 Jan 2024 13:05 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63595 |