Global convergence of quasi‑integral feedback with constant inputs

Prove global convergence of the closed‑loop quasi‑integral feedback control system for gene expression under constant reference inputs and constant disturbances, avoiding reliance on linearization‑based arguments.

Background

For the QIC architecture analyzed, steady‑state tracking under constant inputs has been shown using linearization, but global convergence guarantees for the full nonlinear system are not yet available.

Global results would certify robust perfect adaptation across the entire state space, which is critical for reliable operation in live‑cell contexts with variability.