Observer-Based Proportional Derivative Control for Takagi-Sugeno Fuzzy Singular Systems with Time Delay (Contemporary Mathematics, 2025)
This paper studies an observer-based control problem for Takagi-Sugeno fuzzy singular system with time delay via proportional derivative control scheme. To achieve this, we design a new proportional derivative controller to transform the original problem into the stabilization problem of the new augmented system. In addition, asymmetric Lyapunov-Krasovskii functional and membership-function-dependent method are used to reduce the conservatism. The admissible sufficient conditions of the closed loop system and the calculation methods of observer gain and controller gain are given by using linear matrix inequality. Finally, two examples are given to verify the advantages of the method.
Keywords: Takagi-Sugeno fuzzy systems; observer-based control; asymmetric Lyapunov-Krasovskii functional method; membership-function-dependent approach; proportional derivative control