  Ergodicity and output controllability have been shown to be fundamental
concepts for the analysis and synthetic design of closed-loop stochastic
reaction networks, as exemplified by the use of antithetic integral feedback
controllers. In [Gupta, Briat & Khammash, PLoS Comput. Biol., 2014], some
ergodicity and output controllability conditions for unimolecular and certain
classes of bimolecular reaction networks were obtained and formulated through
linear programs. To account for context dependence, these conditions were later
extended in [Briat & Khammash, CDC, 2016] to reaction networks with uncertain
rate parameters using simple and tractable, yet potentially conservative,
methods. Here we develop some exact theoretical methods for verifying, in a
robust setting, the original ergodicity and output controllability conditions
based on algebraic and polynomial techniques. Some examples are given for
illustration.
