  Controlling stochastic reactions networks is a challenging problem with
important implications in various fields such as systems and synthetic biology.
Various regulation motifs have been discovered or posited over the recent
years, the most recent one being the so-called Antithetic Integral Control
(AIC) motif in Briat et al. (Cell Systems, 2016). Several favorable properties
for the AIC motif have been demonstrated for classes of reaction networks that
satisfy certain irreducibility, ergodicity and output controllability
conditions. Here we address the problem of verifying these conditions for large
sets of reaction networks with fixed topology using two different approaches.
The first one is quantitative and relies on the notion of interval matrices
while the second one is qualitative and is based on sign properties of
matrices. The obtained results lie in the same spirit as those obtained in
Briat et al. (Cell Systems, 2016) where properties of reaction networks are
independently characterized in terms of control theoretic concepts, linear
programming conditions and graph theoretic conditions.
