## Title data

Grüne, Lars:

**Quantitative aspects of the input-to-state stability property.**

*In:* Gilliam, David S. ; Rosenthal, Joachim
,
University of Notre Dame, South Bend, Indiana
(ed.):
Proceedings of the Fifteenth International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002 : University of Notre Dame, South Bend, Indiana, USA, August 12 - 16, 2002. -
South Bend, Indiana
,
2002
. - Article TUA4-4 [Elektronische Ressource]

## Abstract in another language

In this paper we consider quantitative aspects of the input--to--state stability (ISS) property. Our considerations lead to a new variant of ISS, called input--to--state dynamical stability (ISDS), which is based on using a one--dimensional dynamical system for building the class KL function for the decay estimate and for describing the influence of the perturbation. The main feature of ISDS is that it admits a quantitative or gain preserving Lyapunov function characterization. We also show the relation to the original ISS formulation and present several applications.

## 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: | No |

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

Date Deposited: | 01 Mar 2021 14:37 |

Last Modified: | 23 Mar 2021 09:13 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63405 |