New Conditions for Admissibility and Control Design of Takagi-Sugeno Fuzzy Descriptor Systems

The paper discusses the admissibility and controller design of nonlinear systems based on the Takagi-Sugeno descriptor model, which is a well-known system that can represent a wide class of nonlinear systems. Due to the importance of the model, many results on the admissibility problem have been in the literature and have shown the improved results. However, there is still room to reduce the conservativeness of the existing admissibility conditions. In this paper, new admissibility conditions and control design methods are proposed. To this end, new Lyapunov functions, which have an integral structure of the membership functions, are introduced. These classes of Lyapunov functions eventually reduces the conservatism in admissibility and control design conditions. Furthermore, a relaxation lemma is used to further reduce the conservatism. Finally, illustrative examples are given to show the effectiveness of our control design methods.