Globally stabilizing feedback control of process systems in generalized Lotka–Volterra form

In the present paper a globally stabilizing feedback controller design method is proposed for process systems when the feedback structure is also assumed to be in a quasi-polynomial form. It is shown that such feedback structure can always be achieved for process systems.By exploiting the special structure of the controller design problem, the existent iterative linear matrix inequality (ILMI) algorithm of [Y.-Y. Cao, J. Lam, Y.-X. Sun, Static output feedback stabilization: an ILMI approach, Automatica 12 (1998) 1641–1645] is applied to solve the BMI feasibility problem underlying the design.In addition, some partial results on placing the globally stable equilibrium point with respect to the positive orthant have also been proposed that is only possible in a fully actuated situation when the input variables are the intensive variables at the inlet. Furthermore, some preliminary results in selecting the structure of the QP-type feedback have also been presented.