MEMORIZING PROPERTIES OF HYSTERESIS MEDIA

A hysteresis nonlinearity is regarded as an input-output correspondenc e, continuous in the uniform metric and invariant with respect to mono tone changes of time. A class of hysteresis nonlinearities as said to separate two inputs if there exists a nonlinearity, in, this class suc h that the corresponding outputs are different at some finite time. We End a simple class qi ''elementary'' hysteresis nonlinearities with s calar inputs and outputs and a two-dimensional state space that separa tes any pair of inputs that are not equivalent to each other with resp ect to monotone changes of time. Realization theorems proved in the pa per substantiate the possibility of approximation, of scalar hysteresi s operators by special combinations of elementary hysteresis nonlinear ities.