Control of enzymatic reactions via quadratic immersion

One of the aims of Synthetic Biology is to regulate metabolic products for specific biochemical reaction networks. These networks are usually designed as elementary modules to be interconnected each other and efforts are spent to minimize undesired coupling effects arising from the mutual interaction. Within this framework, this note considers a basic enzymatic reaction scheme as an elementary input/output module, with a related specific control problem addressed according to a quadratic immersion, a recently developed control methodology. The quadratic immersion embeds the system equations that model the enzymatic reaction network into an extended, finitedimensional state-space, according to which the control problem may be restated in a simplified version, whose solution guarantees the output asymptotic convergence to a desired value according to a smooth trajectory