Improved Observer Design with Time-Delay Membership Functions for Takagi-Sugeno Fuzzy Systems

The state estimation is important issues in system theory and control systems. Especially, estimation of the state variables of general nonlinear systems is essential but it is still difficult at the same time. This paper proposes design methods for an observer of a nonlinear system described by Takagi-Sugeno(T-S) fuzzy system. Because of the capability of representation of T-S fuzzy system, our observers are designed for a quite large class of nonlinear systems, which cover most systems in various engineering fields. Our observer design employs multiple Lyapunov matrix methods, which result from Lyapunov function candidate with the multiple integrals of the membership functions. Our resulting observers are a nonparallel distributed observer (PDO). This method drastically reduces the conservativeness of observer design conditions. In order to provide the usefulness of our proposed design approach, an illustrative example is provided. Finally, we end with concluding remarks.