Multimodel stabilization based on the state estimation with unmeasurable premise variables of a bioreactor

This paper presents the design of a multi-model state feedback stabilization of a bioreactor. In general, biological models are known by multiple equilibrium that are, in most of the cases, unstable or undesirable. To prevent the system from unstable behaviors and force him to operate properly around an appropriate equilibrium point, a parallel distributed compensation controller based on state estimation with unmeasurable premise variables is designed. We, first, propose to make a change of variables around the desired equilibrium point. Then, based on the Takagi-Sugeno (T-S) formulation, we build a multi-model according to the new state variables. The stability of the whole closed-loop system is studied by using the Lyapunov theory. New stability conditions, in terms of linear matrix inequalities, are then developed. The performance of this approach is illustrated by means of a biomass growth process with Haldane kinetic.