  In this paper, we investigate the well-posedness and positivity property of
infinite-dimensional linear system with unbounded input and output operators.
In particular, we characterize the internal and external positivity for this
class of systems. This latter effort is motivated in part by a complete
description of well-posed positive control/observation systems. An interesting
feature of positive well-posed linear systems is that weak regularity and
strong regularity, in the sense of Salamon and Weiss, are equivalent. Moreover,
we provide sufficient conditions for zero-class admissibility for positive
semigroups. In the context of positive perturbations of positive semigroups, we
establish two perturbation results, namely the Desch-Schappacher perturbation
and the Staffans-Weiss perturbation. As for illustration, these findings are
applied to investigate the existence and uniqueness of a positive mild solution
of the linear Boltzmann equation with non-local boundary conditions on finite
network.
