Robust feedback-control analysis of the Threonine synthesis pathway via various system norms

In this paper we consider the well studied Thre-onine Synthesis pathway in E. Coli, leading from Aspartate to the end product Threonine, via a complex five step mechanism. Following linearization of each step in the pathway around pre-chosen physiologically sound set points, we assemble the (originally nonlinear) system as a linear uncertain polytopic one. We study the effect of the negative feedback-loops that are 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.