Extended Aggregate Observation Drift

Let $l$ and $\tilde{l}$ be \reftext{def:natural-numbers-2026a}{natural numbers} with $l\ge2$ and $\tilde{l}\ge1$, let $\tilde{\beta}$ be an \reftext{def:observation-rate-family-2026a}{observation-rate family} on $l$ states with $\tilde{l}$ observation channels, and let $(\tilde{U},\bar{\tilde{\beta}})$ be a \reftext{def:c2-observation-rate-extension-2026a}{twice continuously differentiable extension} of $\tilde{\beta}$ with derivative bound $\tilde{K}$, points of $\tilde{U}$ being written $\Sigma$ as in that definition.

The \textbf{extended aggregate observation drift} of $(\tilde{U},\bar{\tilde{\beta}})$ is the function $\bar{\tilde{b}}:\tilde{U}\to\mathbb{R}^{\tilde{l}}$ whose components are