Minimal spectral abscissa conjecture for scalar linear systems with two delays

Consider the scalar linear delay system with two delayed feedback terms, with real coefficients $a_0,a_1,a_2$ and positive delays $\tau_1,\tau_2$. Let $\alpha_{\min}$ denote the infimum of the spectral abscissa over the choices of $a_1$ and $a_2$.

Two-delay minimal spectral abscissa conjecture. For arbitrary $a_1,a_2\in\mathbb{R}$, the minimal spectral abscissa is

$$\alpha_{\min}=a_0-\frac{1}{\tau_1}-\frac{1}{\tau_2}.$$

The conjecture proposes that two delayed feedback terms attain the natural extension of the one-delay minimum, supporting the use of multiple delays to improve stability without an explosion in the feedback coefficients. The paper notes that an analogous result for more than two delays may fail without bounds on the delays; the two-delay claim is left as a conjecture.