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| DOI： |
| Received:September 05, 2007 |
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| Periodicity in Delta-modulated feedback control |
| Xiaohua XIA, Guanrong CHEN, Rudong GAI, Alan S.I.ZINOBER |
| (Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria 0002, South Africa;Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China;Department of Computation Science, Huaiyin Institute of Technology, Huai’an Anhui 223001, China;Department of Applied Mathematics, The University of Sheffield, Sheffield S10 2TN, UK) |
| 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. |
| Key words: Switching Periodic orbit Delta-modulation Sign polynomial Nonlinear control |
