Mason–Shorten–Angeli conjecture on stability of positive linear switched systems

Let $A_0,A_1\in \mathbb{R}^{n\times n}$ be Metzler matrices, and consider the positive linear switched system

$$\dot{x}=(uA_0+(1-u)A_1)x,$$

where the switching signal takes values in $\\{0,1\\}$. Assume that $kA_0+(1-k)A_1$ is Hurwitz for every $k\in[0,1]$.

Mason–Shorten–Angeli conjecture. If the system is a positive linear switched system, then this Hurwitz condition is sufficient for global uniform asymptotic stability.

The claim concerns whether a necessary convex-hull stability condition becomes sufficient in the positive setting. The source presents it as a conjecture posed by Mason and Shorten, and independently by David Angeli; no resolution is supplied in the given text.