## Title data

Grüne, Lars:

**Input-to-state dynamical stability and its Lyapunov function characterization.**

*In:* IEEE Transactions on Automatic Control.
Vol. 47
(2002)
Issue 9
.
- pp. 1499-1504.

ISSN 1558-2523

DOI: https://doi.org/10.1109/TAC.2002.802761

## Abstract in another language

We present a new variant of the input-to-state stability (ISS) property 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. We show the relation to the original ISS formulation and describe characterizations by means of suitable Lyapunov functions. As applications, we derive quantitative results on stability margins for nonlinear systems and a quantitative version of a small gain theorem for nonlinear systems

## Further data

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

Refereed: | Yes |

Additional notes: | The preprint that was available until January 25, 2002 (carrying the date May 16, 2001) had a systematic typo in several formulas:
Each inequality of the type DV(x)f(x,u) <= -g(x) (like, e.g., in formula (3.4)) has to be replaced by DV(x)f(x,u) <= -g(V(x)) This error was due to multiple copying and pasting an erroneous formula and has no impact on the proofs and results in this paper, except for some minor changes in the statement and proof of Theorem 3.3. |

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) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) |

Result of work at the UBT: | No |

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

Date Deposited: | 01 Mar 2021 14:31 |

Last Modified: | 23 Mar 2021 09:13 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63403 |