Stability of nonlinear-feedback systems with hysteretic controllers

The paper presents a simple method for deriving frequency-domain-stability criteria for nonlinear-feedback systems which have hysteretic controllers. It is shown that the problem can be resolved by using known results on the stability of multidimensional systems if the hysteresis characteristic is modelled properly. A possible approach to the modelling problem is discussed. This leads to a representation of the hysteresis function in the form f (x, sgn x¿), where sgn x¿ stands for the signum function of the derivative of the input signal. Three different cases of hysteresis are considered in the paper. Numerical examples of each of these are presented, together with experimental data.