{"ID":2830646,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.09474","arxiv_id":"2512.09474","title":"Some Remarks on Positive/Negative Feedback","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 $u=-kx$ ($k \u003e0$) is exponentially stable for all $k \u003e0 $, whereas the lack of exponential instability of the (marginally stable) uncontrolled system is amplified by positive feedback $u=kx$ ($k \u003e0)$. By contrast, for nonlinear systems it is shown, by example, that this intuitive dichotomy may fail to hold.","short_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 $u=-kx$ ($k \u003e0$) is exponentially stable for all $k \u003e0 $, whereas the lack o...","url_abs":"https://arxiv.org/abs/2512.09474","url_pdf":"https://arxiv.org/pdf/2512.09474v3","authors":"[\"Thomas Berger\",\"Achim Ilchmann\",\"Eugene P. Ryan\"]","published":"2025-12-10T09:51:11Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}