Observer Design for Takagi-Sugeno Fuzzy Descriptor System Using a Lyapunov Function with Integrals of the Membership Functions

We discuss an observer design for nonlinear descriptor systems described by Takagi-Sugeno fuzzy descriptor system, which can represent a broader class of systems, including not only differential equations but also algebraic equations, compared to the standard Takagi-Sugeno fuzzy system. The observer design is important to estimate the state of systems because not all states of systems can be measured in many cases. In this paper, we propose a new observer based on a descriptor form and a Lyapunov function candidate structured using integrals of the membership functions to obtain a relaxed observer design condition. Finally, a numerical example is shown to illustrate the comparison of our observer design methods and others based on the conventional Lyapunov functions.