Limit cycles and divergent behavior may be observed in sigma delta modulators (SDMs), especially when the inputs are overloaded. In this paper, we consider high order SDMs as used in A/D and D/A audio applications. Consideration is given as to how the initial states of the SDM affect its stability. The conditions which may give rise to different nonlinear behaviors are derived. Then we develop a novel control algorithm based on fuzzy impulsive control, which involves a decision mechanism for stabilizing different possible instabilities. Examples featuring lowpass and bandpass SDMs of various order are given in order to illustrate the effectiveness of the proposed control strategy.
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