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Homogeneous State Feedback Stabilization of Homogenous Systems

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

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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