This paper considers the

$H_{\infty }$

control problem in the finite-time horizon for a class of T-S fuzzy systems that frequently work under a certain fuzzy rule. By assigning different weights to

$H_{\infty }$

indexes of different subsystems, a novel finite-time membership function-dependent

$H_{\infty }$

performance is proposed. Then, better disturbance rejection can be achieved for this specific type of T-S fuzzy system. In order to save the system resources, an event-triggered mechanism is developed. Different from the widely existing dynamic event-triggered mechanism, a dynamic memory event-triggered mechanism is established by introducing dynamic variables with memory. Rigorous theoretical analysis shows that the proposed dynamic memory event-triggered mechanism possesses larger event-triggered intervals than the existing dynamic event-triggered mechanism. This facilitates the implementation of the proposed scheme in real systems, as real physical components require time intervals between successive event executions. Further, based on the newly proposed index and dynamic memory event-triggered mechanism, the finite-time event-triggered

$H_{\infty }$

control problem of the considered system is solved. Finally, a practical example is employed to display the efficacy of the proposed scheme.

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