## Title data

Grüne, Lars:

**Gain preserving Lyapunov functions for perturbed and controlled systems.**

*In:*
Proceedings of the 41st IEEE Conference on Decision and Control. Volume 1. -
Piscataway, NJ
: IEEE Service Center
,
2002
. - pp. 707-712

ISBN 0-7803-7516-5

DOI: https://doi.org/10.1109/CDC.2002.1184587

## Abstract in another language

Lyapunov functions are an important tool for stability analysis and stabilization of nonlinear systems. They are useful in many ways, e.g., for the design of (robustly) stabilizing feedback laws, for the analysis of the system's behavior and, last but not least, as a technical tool for many proofs involving stability properties of nonlinear systems. In this paper we give Lyapunov function characterizations for suitable variants of the input-to-state stability property, which do not only imply the qualitative properties but also represent the robustness gains and attraction rates. Using techniques from nonsmooth analysis and viscosity solutions of first order PDEs we are in particular able to formulate Hamilton-Jacobi type inequalities which characterize the respective properties.

## 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 14:28 |

Last Modified: | 23 Mar 2021 09:13 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63401 |