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.