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Abstract
This paper considers the stability of a feedback system with backlash. It is assumed that the feedback loop consists of an asymptotically linear, monotonic non-linearity with slope confined to [0, k[, a linear time-invariant sub-system characterized by the impulse response, and a transducer with backlash. A class of input is considered. The stability criterion for the feedback system is given in the form of the multiplier. Such is also the case with systems with an instantaneous non-linearity
A sufficient condition for the existence of such a multiplier are derived in the Xyquist plane
Moreover, different classes of multiplier are derived in the case when the nonlinear amplifier is replaced by a linear amplifier or in the case when the asymptotic linearity restriction on the non-linearity is removed
An example is given to illustrate the proposed stability criterion.
Notes
† Communicated by the Authors.