Some remarks on positive/negative feedback

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 x ̇ = u which, under negative linear feedback u = − k x ( 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 = k x ( k > 0 ). By contrast, for nonlinear systems it is shown, by example, that this intuitive dichotomy may fail to hold.