Stability Analysis of Periodic Solutions in Nonautonomous Systems with Hysteretic Elements.

This paper considers the case where hysteresis is given by the Preisach model and discusses the stability analysis for the periodic solution in the nonautonomous system containing hysteretic elements. The behavior of the system containing hysteretic elements is affected by the history of the system until it arrives at the steady state. In this paper, it is shown first that even periodic solutions with the same hysteretic loop may have different variational systems for the steady-state solution if the histories until arriving at the steady state are different, Next, two kinds of stability criteria are considered based on the difference of the history up to the steady state and the stability against the external disturbance is investigated. The dependence of the stability of the solution on the bifurcation of the periodic solution also is discussed. Finally, examples of numerical analysis are presented to verify the result of discussions. [ABSTRACT FROM AUTHOR]