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Periodic orbits from Δ-modulation of stable linear systems

Xia, X. and Zinober, A. (2004) Periodic orbits from Δ-modulation of stable linear systems. IEEE Transactions on Automatic Control, 49 (8). pp. 1376-1380. ISSN 0018-9286

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Abstract

The Δ-modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by cTx where c ∈Rn/{0} is a given, otherwise arbitrary, vector. We obtain necessary and sufficient conditions for the existence of periodic points of a finite order. Some concrete results about the existence of a certain order of periodic points are also derived. We also study the relationship between certain polyhedra and the periodicity of the Δ-modulated orbit.

Item Type: Article
Copyright, Publisher and Additional Information: © Copyright 2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: Delta-modulation; periodic points; polyhedra; sliding-mode control
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Mrs Megan Hobbs
Date Deposited: 22 Mar 2010 11:21
Last Modified: 08 Feb 2013 17:00
Published Version: http://dx.doi.org/10.1109/TAC.2004.832664
Status: Published
Publisher: Institute of Electrical and Electronics Engineers
Identification Number: 10.1109/TAC.2004.832664
URI: http://eprints.whiterose.ac.uk/id/eprint/10638

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