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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

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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