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

About 12 years old · traced to

Let A0,A1∈Rn×nA_0,A_1\in \mathbb{R}^{n\times n} be Metzler matrices, and consider the positive linear switched system

x˙=(uA0+(1−u)A1)x,\dot{x}=(uA_0+(1-u)A_1)x,

where the switching signal takes values in 0,1\\{0,1\\}. Assume that kA0+(1−k)A1kA_0+(1-k)A_1 is Hurwitz for every k∈[0,1]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.

References

Primary source

Gal Hochma and Michael Margaliot, “High-order maximum principles for the stability analysis of positive bilinear control systems”, arXiv:1407.3437 (2014).

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