Admissibility and Design Issues for T-S Fuzzy Descriptor Systems With Perturbed Derivative Matrices in the Rules

Abstract

This article mainly investigates the admissibility analysis and the parallel distributed compensator (PDC) for fuzzy descriptor systems with perturbed derivative matrices in the rules. The standard Takagi–Sugeno (T–S) fuzzy model is generalized into a fuzzy descriptor model with the perturbed derivative matrices existing in each rule, which can be used to represent a larger class of nonlinear and/or uncertain systems. Based on linear matrix inequalities (LMIs) technique, a new admissibility analysis condition for the considered fuzzy descriptor system is first presented, where the new results involve slack matrices for lessening the conservatism. Furthermore, we further cope with the fuzzy PDC synthesis associated with admissibility and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</i> -admissibility assurance for the resulting closed-loop fuzzy descriptor systems. Since all the proposed criteria can be explicitly formulated in terms of LMIs or parametric LMIs, we can handily verify them via current LMI solvers. Finally, illustrative examples are given to demonstrate that the proposed approach is valid and effective.