  For population systems modeled by age-structured hyperbolic partial
differential equations (PDEs), we redesign the existing feedback laws, designed
under the assumption that the dilution input is directly actuated, to the more
realistic case where dilution is governed by actuation dynamics (modeled simply
by an integrator). In addition to the standard constraint that the population
density must remain positive, the dilution dynamics introduce constraints of
not only positivity of dilution, but possibly of given positive lower and upper
bounds on dilution. We present several designs, of varying complexity, and with
various measurement requirements, which not only ensure global asymptotic (and
local exponential) stabilization of a desired positive population density
profile from all positive initial conditions, but do so without violating the
constraints on the dilution state. To develop the results, we exploit the
relation between first-order hyperbolic PDEs and an equivalent representation
in which a scalar input-driven mode is decoupled from input-free
infinite-dimensional internal dynamics represented by an integral delay system.
