Math. Model. Nat. Phenom.
Volume 15, 2020
Systems with Hysteresis and Switching
|Number of page(s)||12|
|Published online||11 November 2020|
On stability of linear dynamic systems with hysteresis feedback
Faculty of Engineering and Science, University of Agder, p.b. 422,
* Corresponding author: firstname.lastname@example.org
Accepted: 6 April 2020
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.
Mathematics Subject Classification: 74N30 / 34C55 / 34D23 / 34K20 / 34K35 / 93C10 / 93D10
Key words: Hysteresis / nonlinear systems / stability / dissipativity
© The authors. Published by EDP Sciences, 2020
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