Membership Function-Dependent $H_{\infty }$ Control for Set-Described T-S Fuzzy System via Improved Dynamic Memory Event-Triggered Mechanism

In this article, we address the $H_{\infty }$ control problem for a class of Takagi-Sugeno (T-S) fuzzy systems, where the premise variables often work in some fuzzy sets. By combining the properties of the product inference engine and set theory, we develop a membership function-dependent $H_{\infty }$ index, enhancing disturbance suppression by assigning diverse weights to various subsystem $H_{\infty }$ indices. An advanced event-triggered mechanism, utilizing dynamic memory variables, is proposed to expand the threshold and conserve resources, outperforming conventional dynamic event-triggered mechanisms (DETM). Theoretical analysis indicates that the dynamic memory event-triggered mechanism (DMETM) offers a more extensive event-triggered interval than the conventional memoryless DETM. Furthermore, in the proposed DMETM, a system-related dynamic variable is designed to replace the corresponding constant coefficient, increasing design flexibility and relaxing the design constraints of current state-of-the-art DETMs. Specifically, by constructing a monotonic nonincreasing bounded function, the system information is successfully integrated into the design of the dynamic coefficient. This design allows the threshold of the event-triggered condition to be adjusted more flexibly according to the system's operational status, thereby improving the practicality of the scheme in real-world applications. Besides, Zeno behavior is avoided. Finally, the effectiveness of the scheme is verified by an example.