Ergodicity, Output-Controllability, and Antithetic Integral Control of Uncertain Stochastic Reaction Networks

The ergodicity and the output-controllability of stochastic reaction networks have been shown to be essential properties to fulfill to enable their control using, for instance, antithetic integral control (Briat, Gupta, Khammash, “Antithetic integral feedback ensures robust perfect adaptation in noisy biomolecular networks,” Cell Syst., vol. 2, pp. 17-28, 2016). We propose here to extend those properties to the case of uncertain networks. To this aim, the notions of interval, robust, sign, and structural ergodicity/output-controllability are introduced. The obtained results lie in the same spirit as those obtained in [1], where those properties are characterized in terms of control theoretic concepts, linear algebraic conditions, linear programs, and graph-theoretic/algebraic conditions. An important conclusion is that all those properties can be characterized by linear programs. Two examples are given for illustration.