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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.09474 |
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| _version_ | 1866910028152176640 |
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| author | Berger, Thomas Ilchmann, Achim Ryan, Eugene P. |
| author_facet | Berger, Thomas Ilchmann, Achim Ryan, Eugene P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some Remarks on Positive/Negative Feedback Berger, Thomas Ilchmann, Achim Ryan, Eugene P. Optimization and Control 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. |
| title | Some Remarks on Positive/Negative Feedback |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2512.09474 |