Finite-Time Membership Function-Dependent $H_{\infty }$ Control for T–S Fuzzy Systems via a Dynamic Memory Event-Triggered Mechanism
Qinghua Hou, Jiuxiang Dong
Abstract
This article considers the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control problem in the finite-time horizon for a class of Takagi–Sugeno (T–S) fuzzy systems that frequently work under a certain fuzzy rule. By assigning different weights to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> indexes of different subsystems, a novel finite-time membership-function-dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> 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. Furthermore, based on the newly proposed index and dynamic memory event-triggered mechanism, the finite-time event-triggered <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control problem of the considered system is solved. Finally, a practical example is employed to display the efficacy of the proposed scheme.