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.
Xiaohua XIAGuanrong CHENRudongGAIAlan S. I. ZINOBER
