On stability of linear dynamic systems with hysteresis feedback
Journal article, Peer reviewed
Accepted version
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https://hdl.handle.net/11250/2654968Utgivelsesdato
2020Metadata
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Originalversjon
Ruderman, M. (2020) On stability of linear dynamic systems with hysteresis feedback In: Mathematical Modelling of Natural Phenomena. 15(2). 12p. DOI:Sammendrag
Abstract. The stability of linear dynamic systems with hysteresis in feedback is considered. While
the absolute stability for memoryless nonlinearities (known as Lure’s problem) can be proved by the
well-known circle criterion, the multivalued rate-independent hysteresis poses significant challenges
for feedback systems, especially for proof of convergence to an equilibrium state correspondingly set.
The dissipative behavior of clockwise input-output hysteresis is considered with two boundary cases of
energy losses at reversal cycles. For upper boundary cases of maximal (parallelogram shape) hysteresis
loop, an equivalent transformation of the closed-loop system is provided. This allows for the application
of the circle criterion of absolute stability. Invariant sets as a consequence of hysteresis are discussed.
Several numerical examples are demonstrated, including a feedback-controlled double-mass harmonic
oscillator with hysteresis and one stable and one unstable poles configuration.