Admissibility and admissibilization for nonlinear singular systems based on T-S fuzzy singular models with different derivative matrices

The admissibility analysis and synthesis problems of nonlinear descriptor systems through extended T-S fuzzy singular systems with different derivative matrices are investigated. By designing the fuzzy Lyapunov function framework and introducing relaxation matrices, a novel and relaxed sufficient condition is presented to guarantee the admissibility of these systems without requiring bounds on the derivative of the membership function. Moreover, by establishing an admissibility equivalence between the original system and its dual system, a design theorem for the fuzzy parallel distribution compensation controller of fuzzy singular systems is proposed using strict linear matrix inequalities. This method is not only easy to implement, but also applicable to a wide range of similar problems. The effectiveness of the main results presented in this paper is illustrated through three illustrative examples.