State-Difference Feedback Control for Discrete-Time Takagi–Sugeno Fuzzy Descriptor Systems with Parameter Uncertainties and External Noises

Abstract

This research focuses on the development of state-difference feedback controllers for discrete-time (DT) nonlinear descriptor systems. Discrete-time nonlinear DA systems consist of difference and algebraic equations and play a crucial role in describing dynamic behavior and capturing the constraints or relationships within the system. However, analytical stability may pose additional challenges due to the unique characteristics of the system. Utilizing fuzzy model-based techniques, the DT nonlinear DA system discussed in this study can be effectively represented using the Takagi–Sugeno (T-S) fuzzy model. After linearizing the nonlinear system through the T-S fuzzy model, traditional linear control techniques become applicable. These techniques are then applied to T-S fuzzy systems to establish stability criteria. This article chooses the Lyapunov function as the method used to analyze system stability. Additionally, we use a free-weighting matrix to introduce additional degrees of freedom. In summary, this paper presents simulation results and discussions to verify the effectiveness of the proposed design approach.