A model representing scalar hysteretic systems with wipe-out memory is prop
osed. In this model a hysteresis operator is represented as a power series
expansion containing an infinite number of terms in general. It is shown th
at this representation converges to any given hysteresis relation having wi
pe-out memory as long as the output of the given hysteresis varies sufficie
ntly smoothly with input history. (C) 2001 American Institute of Physics.