New conditions for stability and stabilizaion of Takagi-Sugeno fuzzy systems

The paper discusses the stability and stabilization of nonlinear systems based on Takagi-Sugeno models, which are a well-known system that can represent a wide class of nonlinear systems. Due to the importance of the models, many results on the stability problem have been in the literature and they have shown their progressive methods. However, there is still room to reduce the conservativeness of the existing stability conditions. In this paper, new stability conditions and control design methods are proposed. To this end, a new Lyapunov function, which has an integral structure of the membership function, is introduced. This structural Lyapunov function eventually reduces the conservatism in stability and stabilizability conditions. On top of that, descriptor system approach and generalized relaxation lemma are employed to further reduce the conservatism. Finally, an illustrative example is given to show the effectiveness of our control design methods.