Hysteretic systems and step-convergent semistability

Hysteresis is usually characterized as a memory-dependent relationship between inputs and outputs. While various operator models have been proposed, it is often convenient for engineering applications to approximate hysteretic behavior by means of finite-dimensional differential models. In the present paper we show that step-convergent semistable systems (that is, semistable systems with convergent step response) give rise to multiple-valued maps under quasi-static operation. By providing a connection between semistability and hysteresis, our goal is to provide a class of differential models for representing hysteretic behavior.