Robust polytopic analysis of the feedback-control of Glycolysis in yeasts via some system norms

In this paper we consider a well studied model of Glycolysis in yeast cells, leading from Glucose to the end product Ethanol, via a minimal nine steps mechanism. We first linearize each step in the pathway around a given set point and we then assemble the (originally nonlinear) system as a linear system subject to various polytopic uncertainties. We study the effect of the negative feedback-loop that is internally exerted on the system. We then probe the sensitivity of the system to variations in certain variables in order to asses the possible optimality of the system in the H₂, H_∞ and the L₂ - L_∞, L_∞ - L_∞ senses.