Event collisions in systems with delayed switches

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Event collisions in systems with delayed switches

Please use this identifier to cite or link to this item: http://hdl.handle.net/10036/3679


Title: Event collisions in systems with delayed switches
Author: Sieber, J.
Kowalczyk, P.
Citation: Proceedings of the 6th IFAC Workshop on Time Delay Systems, L'Aquila, Italy, 10-12 July 2006. Vol. 6, part 1
Publisher: Elsevier
Journal: IFAC-PapersOnLine
Date Issued: 2006
URI: http://hdl.handle.net/10036/3679
DOI: 10.3182/20060710-3-IT-4901.00012
Links: http://dx.doi.org/10.3182/20060710-3-IT-4901.00012
Abstract: We study dynamical systems that switch between two different vector fields depending on a discrete variable. If the two vector fields have linearly unstable fixed points and the switch is subject to a hysteresis and to a delay one expects the system to switch periodically back and forth between the two vector fields, always switching at certain submanifolds of the state space. This is true as long as the delay is sufficiently small. When the delay reaches a problem-dependent critical value so-called event collisions occur. We show that at these event collisions the switching manifolds can increase their dimension, giving rise to higher-dimensional dynamics near the periodic orbit than expected. In many practical applications such as control engineering the dynamical system has additional symmetry, which adds difficulty in the analysis because event collisions generically occur at several points along the periodic orbit simultaneously.
Type: Article
Description: Copyright © 2006 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in IFAC-PapersOnLine, DOI: 10.3182/20060710-3-IT-4901.00012
Keywords: hybrid dynamical systemdelayed switchnon-smooth map
ISSN: 1474-6670

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