Nonlinear feedback models of hysteresis

In the present article we investigate multistability and hysteresis within the context of linear systems with nonlinear feedback. For concreteness and simplicity, we focus primarily on single-input, single-output linear systems with companion-form realizations. For various choices of the realization parameters, we characterize the input-output equilibria set. We analyze this set in detail for the case of a deadzone nonlinearity, and we determine the values of the realization parameters that give rise to traversal-type or bifurcation-type hysteresis. The rich diversity of hysteretic phenomena that can be generated by interconnecting a linear system with a feedback nonlinearity is the motivation for this article.