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arXiv · 2512.09474

Some Remarks on Positive/Negative Feedback

Thomas Berger·Achim Ilchmann·Eugene P. Ryan
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Abstract

In the context of linear control systems, a commonly-held intuition is that negative and positive feedback cannot both be stability enhancing. The canonical linear prototype is the scalar system $\dot x=u$ which, under negative linear feedback $u=-kx$ ($k >0$) is exponentially stable for all $k >0 $, whereas the lack of exponential instability of the (marginally stable) uncontrolled system is amplified by positive feedback $u=kx$ ($k >0)$. By contrast, for nonlinear systems it is shown, by example, that this intuitive dichotomy may fail to hold.

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Thomas Berger, Achim Ilchmann, Eugene P. Ryan. 2025-12-10. Some Remarks on Positive/Negative Feedback. https://arxiv.org/abs/2512.09474

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