Reference for a uniform spectral radius bound

Identify a citable reference that proves a uniform version of the spectral radius formula ensuring a uniform exponential bound on powers of a matrix‑valued function A(z) over a compact parameter set K when sup_{z in K} p(A(z)) < r.

Background

To control characteristic functions uniformly over parameter ranges, the paper uses a uniform spectral radius bound analogous to the spectral radius formula. The authors provide a proof but explicitly state they do not know a prior reference.

Documenting an existing source (if any) would clarify provenance and potentially strengthen connections to established operator theory results.