Some remarks on positive/negative feedback

Thomas Berger; Achim Ilchmann; Eugene P. Ryan

doi:10.1016/j.sysconle.2026.106394

Some remarks on positive/negative feedback

Thomas Berger, Achim Ilchmann, Eugene P. Ryan

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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 ẋ=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.

Original language	English
Article number	106394
Journal	Systems and Control Letters
Volume	211
Early online date	22 Feb 2026
DOIs	https://doi.org/10.1016/j.sysconle.2026.106394
Publication status	E-pub ahead of print - 22 Feb 2026

Data Availability Statement

No data was used for the research described in the article.

Keywords

Nonlinear control systems
Positive and negative feedback

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

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10.1016/j.sysconle.2026.106394Licence: CC BY

Cite this

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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 ẋ=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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AU - Ilchmann, Achim

AU - Ryan, Eugene P.

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N2 - 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 ẋ=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.

AB - 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 ẋ=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.

KW - Nonlinear control systems

KW - Positive and negative feedback

UR - https://www.scopus.com/pages/publications/105030487811

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DO - 10.1016/j.sysconle.2026.106394

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VL - 211

JO - Systems and Control Letters

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ER -

Some remarks on positive/negative feedback

Abstract

Data Availability Statement

Keywords

ASJC Scopus subject areas

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