On a Class of Hysteretic, Dynamical Systems with Application to Smart Material Actuators∗

A class of dynamical systems with hysteresis is considered, where the hysteresis nonlinearity is coupled to an ordinary differential equation (ODE) in an unusual manner. Such systems arise in various contexts, e.g., smart material modeling, open-loop control of smart material actuators, and feedback control of systems involving hysteretic components. In this paper the Preisach operator is used to represent the hysteresis. The well-posedness of the hysteretic systems is established under general assumptions. With more specific assumptions, a number of system-theoretic properties are analyzed, including reachability, observability, input-output stability, and stability of equilibria. Existence of periodic solutions under a periodic input is shown. Finally numerical integration of such systems is discussed.