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Homogeneous state feedback stabilization of homogeneous systems

Name: Homogeneous state feedback stabilization of homogeneous systems
Creator: Lars Grüne
Keywords: 0209 industrial biotechnology, Homogeneous system, Lyapunov exponents, 500, 02 engineering and technology, 01 natural sciences, stabilization, 510, State feedback stabilization, Control Lyapunov functions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2000Publisher:IEEEJournal:Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), volume 4, pages 3,409-3,414

Authors: Lars Grüne;

doi: 10.1109/cdc.2000.912230 , 10.1137/s0363012998349303 , 10.15495/epub_ubt_00005466 , 10.15495/epub_ubt_00005465

Homogeneous state feedback stabilization of homogeneous systems

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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.

Related Organizations

University of Bayreuth
Germany
Goethe University Frankfurt
Germany

Keywords

Homogeneous system, Lyapunov exponents, 500, stabilization, 510, State feedback stabilization, Control Lyapunov functions, homogeneous feedback, Lyapunov and storage functions, Stabilization of systems by feedback, Characteristic and Lyapunov exponents of ordinary differential equations, discretized feedback, control Lyapunov function

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	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	132
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