Admissibility Analysis and Robust H∞ Control for T-S Fuzzy Descriptor Systems With Structured Parametric Uncertainties

This article considers admissibility analysis and robust H-infinity control for continuous-time Takagi-Sugeno fuzzy descriptor systems with norm-bounded uncertainties in all parametric matrices. The system under consideration contains singular derivative matrices and different membership functions, thus it generalizes other related forms. First, uncertainties in derivative matrices are divided into two cases, i.e., one is expressed by a constant matrix left multiplied by an invertible uncertain matrix and the other is produced by its dual form. Then, admissible conditions and H-infinity performance for the system with the first case of uncertainties are derived based on a new augmented system. As for the second case, the admissibility analysis is converted into the first case by an equivalent companion system then solved as well. All conditions are cast into strict linear matrix inequalities. Besides, due to the introduction of a new nonquadratic fuzzy Lyapunov function and slack decision variables, the proposed methods are less conservative than related ones. Finally, simulation examples are provided to illustrate improvements and effectiveness of the main results.

Automated summary

This article investigates admissibility analysis and robust H-infinity control for fuzzy descriptor systems with norm-bounded uncertainties in parametric matrices. The uncertainties are categorized into two cases, leading to the derivation of admissible conditions and performance criteria for different scenarios. The proposed methods, utilizing strict linear matrix inequalities and a new Lyapunov function, demonstrate improved conservatism compared to existing approaches, as highlighted through simulation examples.