H∞ feedback-control of the Threonine Synthesis pathway via system uncertainty

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