Convex upper bounds for robustness of positive systems

A positive system is a system whose relevant system matrices have nonnegative entries. Let $\boldsymbol{\Delta}$ be a causal, diagonal, linear time-varying uncertainty, and suppose it is bounded by

$$\|\boldsymbol{\Delta}\| = \|\boldsymbol{\delta}_1\|_\infty + \|\boldsymbol{\delta}_2\|_\infty + \cdots + \|\boldsymbol{\delta}_n\|_\infty.$$

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

The claim suggests that robustness analysis for positive systems can be bounded by a tractable convex optimization problem, complementing the paper's discussion of stationary inputs and scalable matrix-based analysis. The source does not specify a proof or a precise general class beyond positive systems and the stated uncertainty norm.