H_∞ feedback control of biochemical pathways via system uncertainty

In this study we consider a simple unbranched enzyme pathway, composed of four blocks of a simple Michaelis-Menten enzymes, each of which operates around a pre-chosen set point. We then assemble the (originally nonlinear) system as a linear uncertain polytopic one. In the closed-loop configuration we study the effect of a negative feedback-loop that is internally exerted on the system by a self product of the pathway. We then probe the sensitivity of the system to variations in certain variables to asses the possible optimality of the system, in the H_∞ sense. We demonstrate the applicability of our results via a realistic example.