Robust<i>H</i><sub>∞</sub>output feedback control for type‐2<scp>Takagi‐Sugeno</scp>fuzzy systems with multiple time‐delays and disturbances: A descriptor redundancy approach
Wei Zheng, Zhiming Zhang, Fuchun Sun, Shuhuan Wen, Xiaolei Li, Hongbin Wang
Abstract
Abstract The H ∞ stability analysis and interval type‐2 Takagi‐Sugeno (T‐S) fuzzy control is studied for a class of interval type‐2 T‐S fuzzy systems. Firstly, the interval type‐2 T‐S fuzzy model is employed to approximate the system plant. Secondly, the delay‐dependent interval type‐2 T‐S fuzzy dynamic output feedback controller is designed. Thirdly, two classes of stability conditions in terms of linear matrix inequalities (LMIs) are derived, and the closed‐loop system is asymptotically stable and prescribed H ∞ performance is achieved. The delay‐dependent interval type‐2 T‐S fuzzy dynamic output feedback controller is designed to relax the control design conditions. The descriptor redundancy method is employed for avoiding the crossing vectors between the system gain matrices and controller gain matrices. The delay‐dependent Lyapunov functional with descriptor redundancy matrix is introduced, and the upper and lower membership functions information is considered. Some slack matrices are introduced via the upper and lower membership functions information to solve the obtained LMIs. Finally, simulation examples are performed to show the effectiveness of the proposed methods.