  There are several results on the stability of nonlinear positive systems in
the presence of time delays. However, most of them assume that the delays are
constant. This paper considers time-varying, possibly unbounded, delays and
establishes asymptotic stability and bounds the decay rate of a significant
class of nonlinear positive systems which includes positive linear systems as a
special case. Specifically, we present a necessary and sufficient condition for
delay-independent stability of continuous-time positive systems whose vector
fields are cooperative and homogeneous. We show that global asymptotic
stability of such systems is independent of the magnitude and variation of the
time delays. For various classes of time delays, we are able to derive explicit
expressions that quantify the decay rates of positive systems. We also provide
the corresponding counterparts for discrete-time positive systems whose vector
fields are non-decreasing and homogeneous.
