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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, &#x201C;Antithetic integral feedback ensures robust perfect adaptation in noisy biomolecular networks,&#x201D; 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.

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