Robust peak to peak and H_∞ static output-feedback control of the Threonine Synthesis pathway

In this paper we extend previous attempt to explore the possible robustness of the Threonine Synthesis pathway in the H_∞ and the L_∞-L_∞ senses. Following linearization of the pathway kinetic equations, two modelling strategies are applied the first of which tests the robustness of the nominal linearized system to various parameter uncertainties, including uncertainties in the control gain matrix of the system. In the second strategy similar tests of the latter are applied however, the original nonlinear system is modelled as an uncertain linear system where the extent of nonlinearity is tuned by the uncertainty interval. It is shown that the system sensitivity to the various uncertain parameters agree in both strategies and that the two system performance indices, the H_∞ and the L_∞-L_∞ better represents the system behavior compared to experimental results that were obtained for the Threonine Synthesis pathway.