Stability of dithered non-linear systems with backlash or hysteresis†

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Abstract
We study the effect of dither on the non-linear element of a single-input single-outout feedback system. We consider non-linearities with memory (backlash, hysteresis), in the feedforward loop; a dither of a given amplitude is injected at the input of the non-linearity. The non-linearity is followed by a linear element with low-pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the non-linearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system stability guarantees that of the given hysteretic system

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