Sufficient conditions for rate-independent hysteresis in autoregressive identified models

This paper shows how hysteresis can be described using polynomial models and what are the sufficient conditions to be met by the model in order to have hysteresis. Such conditions are related to the model equilibria, to the forcing function and to certain term clusters in the polynomial models. The main results of the paper are used in the identification and analysis of nonlinear models estimated from data produced by a magneto-rheological damper (MRD) model with Bouc-Wen rate-independent hysteresis. A striking feature of the identified model is its simplicity and this could turn out to be a key factor in controller design.