Duhem Feedback and Friction-Induced Staircase Hysteresis

In this paper we provide a system-theoretic picture of the hysteresis induced by friction. We study the hysteretic response of a linear system connected with a Duhem hysteretic model in the feedback. We then use the popular Dahl and LuGre Duhem friction models to model the mass-spring system with friction, as a linear system with Duhem feedback. We use the feedback model to study the hysteretic response between the external force applied on the mass and the displacement of the mass.