Absolute stability analysis of linear systems with Duhem hysteresis operator

In this paper, we investigate the stability of positive and negative feedback interconnections of a linear system and a Duhem hysteresis operator. We provide sufficient conditions on the linear plant and on the Duhem operator which are based on the counterclockwise (CCW) or clockwise (CW) input–output property of the plant and hysteresis operator. We show the application of our main result in the design of a linear controller to stabilize a simple mechanical system driven by a hysteretic actuator, such as, piezo-actuator or smart material-based actuator.