## Title data

Grüne, Lars:

**Homogeneous State Feedback Stabilization of Homogenous Systems.**

*In:* SIAM Journal on Control and Optimization.
Vol. 38
(2000)
Issue 4
.
- pp. 1288-1308.

ISSN 1095-7138

DOI: https://doi.org/10.1137/S0363012998349303

## Related URLs

## Abstract in another language

We show that for any asymptotically controllable homogeneous system in euclidian space (not necessarily Lipschitz at the origin) there exists a homogeneous control Lyapunov function and a homogeneous, possibly discontinuous state feedback law stabilizing the corresponding sampled closed loop system. If the system satisfies the usual local Lipschitz condition on the whole space we obtain semi-global stability of the sampled closed loop system for each sufficiently small fixed sampling rate, if the system satisfies a global Lipschitz condition we obtain global exponential stability for each sufficiently small fixed sampling rate. The control Lyapunov function and the feedback are based on the Lyapunov exponents of a suitable auxiliary system and admit a numerical approximation.

## Further data

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

Refereed: | Yes |

Keywords: | Homogeneous system; State feedback stabilization; Control Lyapunov functions; Lyapunov exponents; homogeneous feedback; stabilization; discretized feedback |

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 > 510 Mathematics |

Date Deposited: | 22 Feb 2021 08:53 |

Last Modified: | 07 May 2021 07:09 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63265 |