  We show that a sub-homogeneous positive monotone system with bounded
heterogeneous time-varying delays is globally asymptotically stable if and only
if the corresponding delay-free system is globally asymptotically stable. The
proof is based on an extension of a delay-independent stability result for
monotone systems under constant delays by Smith to systems with bounded
heterogeneous time-varying delays. Under the additional assumption of
positivity and sub-homogeneous vector fields, we establish the aforementioned
delay insensitivity property and derive a novel test for global asymptotic
stability. If the system has a unique equilibrium point in the positive
orthant, we prove that our stability test is necessary and sufficient.
Specialized to positive linear systems, our results extend and sharpen existing
results from the literature.
