5 problems

Fortuna's conjecture. The solution $X$ is entrywise nonnegative.

Let $A_0,A_1\in M_d(\mathbb{R})$ be Metzler matrices defining a linear switched system. A counterexample to the question of whether exponential convergence to zero for all trajecto…

Let a positive linear switched system (PLS) be a switched linear system whose subsystem matrices preserve the positive cone, and let GUAS mean globally uniformly asymptotically sta…

Convex upper-bound conjecture. For positive systems, there exists a convex upper bound for a robustness measure against such uncertainties.

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