Robust and structural ergodicity analysis of stochastic biomolecular networks involving synthetic antithetic integral controllers

摘要

Ergodicity and output controllability have been shown to be fundamentalconcepts for the analysis and synthetic design of closed-loop stochasticreaction networks, as exemplified by the use of antithetic integral feedbackcontrollers. In [Gupta, Briat & Khammash, PLoS Comput. Biol., 2014], someergodicity and output controllability conditions for unimolecular and certainclasses of bimolecular reaction networks were obtained and formulated throughlinear programs. To account for context dependence, these conditions were laterextended in [Briat & Khammash, CDC, 2016] to reaction networks with uncertainrate parameters using simple and tractable, yet potentially conservative,methods. Here we develop some exact theoretical methods for verifying, in arobust setting, the original ergodicity and output controllability conditionsbased on algebraic and polynomial techniques. Some examples are given forillustration.