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The innocuousness property of a controller is that property that makes theclosed-loop system stable regardless the values of the controller parameters.In other words, the closed-loop system exhibits some structural stabilityproperty with respect to the parameters of the controller. The innocuousnessproperty was first emphasized in [Briat, Gupta, and Khammash, Cell Systems,2016] where it was shown that for stochastic unimolecular networks, theAntithetic Integral Controller (AIC) is innocuous under very mild conditions onthe controlled network; namely the ergodicity and the output-controllability ofthe open-loop network, and the admissibility of the set-point value. We showhere that the class of p-type AIC controllers arising in the use of AntitheticIntegral Rein Controllers (AIRC) also exhibit such a property. It is shown inthe unimolecular reaction network case that the closed-loop network isstructurally stable with respect to the controller parameters provided that theopen-loop dynamics is stable and that the set-point is admissible. Thoseresults are then extended to the case of so-called output unstable linearsystems and to stable nonlinear networks. Analogous results are obtained forexponential and logistic integral controllers. Some examples are given forillustration.

On the Innocuousness of Deterministic p-type Antithetic Integral Controllers Arising in Integral Rein Control