Estimation of extremal properties of complex networks of linear systems is, in general, a difficult task. In this note such estimation problems are solved for an important class of systems, namely for stable non-negative networks consisting of non-negative sums and convolutions of linear time-invariant systems with non-negative impulse responses. In particular, the problem of estimating the l(1) norm of a stable non-negative system, from rather arbitrary input-output data, is analysed in detail.