Asymptotic Stability Analysis of Lur’e Systems with Butterfly Hysteresis Nonlinearities

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We study the asymptotic stability of Lur’e systems with butterfly hysteresis nonlinearities modeled by the Preisach operators with respect to a set of equilibrium points. We present the input-output rate property of the Preisach operators that exhibit butterfly hysteresis behavior. Based on this characterization, we present sufficient conditions on the linear systems that guarantee the asymptotic stability of the closed-loop system to a set of equilibrium points via circle criterion. Finally numerical simulations are presented to demonstrate these results.
Original languageEnglish
Pages (from-to)349-354
Number of pages6
JournalIEEE Control Systems Letters
Issue number2
Publication statusPublished - 2019


  • Stability of nonlinear systems
  • nonlinear output feedback
  • mechatronics

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