Abstract
Δ-modulated feedback control of a linear system introduces nonlinearity into the system through switchings between two input values. It has been found that Δ-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. Further extensions relate to the existence of periodic points arising from Δ-modulated feedback control of a stable linear system in an arbitrary direction, for which some necessary and sufficient conditions are given.
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