Publications by the same author
plus in the repository
plus in Google Scholar

Bibliografische Daten exportieren
 

Homogeneous State Feedback Stabilization of Homogenous Systems

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005466
URN to cite this document: urn:nbn:de:bvb:703-epub-5466-4

Title data

Grüne, Lars:
Homogeneous State Feedback Stabilization of Homogenous Systems.
Bayreuth , 2000

[thumbnail of gruene_siam_jco_2000_ps-1.pdf]
Format: PDF
Name: gruene_siam_jco_2000_ps-1.pdf
Version: Published Version
Available under License Creative Commons BY 4.0: Attribution
Download (366kB)

Abstract

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: Preprint, postprint
Additional notes (visible to public): erschienen In:
SIAM Journal on Control and Optimization. Bd. 38 (2000) Heft 4 . - S. 1288-1308
Keywords: Homogeneous system; State feedback stabilization; Control Lyapunov functions; Lyapunov exponents; homogeneous feedback; stabilization; discretized feedback
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: 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
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)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5466-4
Date Deposited: 07 May 2021 07:08
Last Modified: 07 May 2021 07:09
URI: https://epub.uni-bayreuth.de/id/eprint/5466