Observer Design for a Class of Takagi-Sugeno Descriptor Systems: Application to an Aerobic Culture of a Recombinant Yeast

In this paper, based on the Takagi-Sugeno (T-S) fuzzy approach with unmeasurable premise variables, our aim consists in developing an observer algorithm permitting to estimate the unknown states for a class of fuzzy descriptor systems. The approach used to solve this problem consists in designing a fuzzy observer described by differential equations only. The idea of the proposed result is to separate the dynamic relations of the static relations in the descriptor model. First, the method used for decomposed the differential part of the algebraic part is developed, secondly we give a fuzzy observer design permitting to estimate the unknown states. The convergence of the state estimation error is studied using the Lyapunov theory and the stability condition is given in term of only one Linear Matrix Inequalitie (LMI). Finally, an application to a descriptor model of an aerobic culture of a recombinant yeast is given in order to illustrate the performance of the proposed fuzzy designed observer.