  It is known that input-output approaches based on scaled small-gain theorems
with constant $D$-scalings and integral linear constraints are non-conservative
for the analysis of some classes of linear positive systems interconnected with
uncertain linear operators. This dramatically contrasts with the case of
general linear systems with delays where input-output approaches provide, in
general, sufficient conditions only. Using these results we provide simple
alternative proofs for many of the existing results on the stability of linear
positive systems with discrete/distributed/neutral time-invariant/-varying
delays and linear difference equations. In particular, we give a simple proof
for the characterization of diagonal Riccati stability for systems with
discrete-delays and generalize this equation to other types of delay systems.
The fact that all those results can be reproved in a very simple way
demonstrates the importance and the efficiency of the input-output framework
for the analysis of linear positive systems. The approach is also used to
derive performance results evaluated in terms of the $L_1$-, $L_2$- and
$L_\infty$-gains. It is also flexible enough to be used for design purposes.
