Exact invertible hysteresis models based on play operators

The present paper considers the definition of a class of hysteresis models, based on the superposition of play operators, which can be used to describe magnetic materials and superconductors. As a first step, the paper defines a class of non-local hysteresis models having an inverse operator in a closed form. That class specifies a Preisach model for which the exact inverse is defined. In this frame such a result is a generalization of the well-known result by Krejci. Moreover, a self-contained identification procedure is further addressed by using data measured either on magnetic materials and on superconductors.