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Periodicity in Delta-Modulated feedback control

Xia, X., Chen, G., Gai, R. and Zinober, A.S.I. (2008) Periodicity in Delta-Modulated feedback control. Journal of Control Theory and Applications, 6 (1). pp. 37-44. ISSN 1993-0623

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Abstract

The Delta-modulated feedback control of a linear system introduces nonlinearity into the system through switchings between two input values. It has been found that Delta-modulation gives rise to periodic orbits. The existence of periodic points of all orders of Sigma-Delta modulation with “leaky” integration is completely characterized by some interesting groups of polynomials with “sign” coefficients. The results are naturally generalized to Sigma-Delta modulations with multiple delays, Delta-modulations in the “downlink”, unbalanced Delta-modulations and systems with two-level quantized feedback. Further extensions relate to the existence of periodic points arising from Delta-modulated feedback control of a stable linear system in an arbitrary direction, for which some necessary and sufficient conditions are given.

Item Type: Article
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Mrs Megan Hobbs
Date Deposited: 09 Mar 2010 15:20
Last Modified: 07 Jun 2010 11:09
Published Version: http://dx.doi.org/10.1007/s11768-008-7192-x
Status: Published
Publisher: Springer on behalf of South China University of Technology and Academy of Mathematics and Systems Science, CAS
Identification Number: 10.1007/s11768-008-7192-x
URI: http://eprints.whiterose.ac.uk/id/eprint/10482

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