Stability of nonlinear feedback systems with backlash

A frequency domain stability criterion is given for a feedback system whose loop consists of an instantaneous nonlinear amplifier, a linear dynamical system, and a transducer with backlash. A class of input signals is considered that essentially consists of constant-amplitude functions and exponentially decaying functions. Separate considerations are given to the case when the system includes a saturating instantaneous amplifier and the case when the nonlinear amplifier is not a saturating type. In both cases a single criterion guarantees the stability. A few examples are given to illustrate the proposed stability criterion. Finally it is shown that the stability criterion can be applied to a large class of autonomous non-linear feedback systems containing a nonlinearity with dead-zone or with hysteresis and dead-zone.