Observer-based robust nonfragile H∞ control for uncertain T-S fuzzy singular systems

This paper aims to study the robust nonfragile H∞ controller design problem for a class of uncertain discrete-time nonlinear singular systems. A Takagi-Sugeno (T-S) fuzzy singular model with norm-bounded uncertainties is employed to represent a nonlinear plant. Basing on observers for the fuzzy model, we can construct a fuzzy controller with uncertainties existing in the implementation process. A augmented fuzzy closed-loop system can be obtained by the descriptor systems approach, which can avoid the appearance of coupling terms between matrices of the system model and the controller. Attention of the paper lies in deriving the design conditions of the observer-based controller by choosing a fixed common and fuzzy Lyapunov function, respectively, such that the admissibility and the prescript H∞ performance of the augmented closed-loop system can be guaranteed. Finally, the simulation results show the validity of the proposed methods.