Weighted Memory <i>H</i> <sub>∞</sub> Stabilization of Time-Varying Delayed Takagi–Sugeno Fuzzy Systems
Shen Yan, Zhou Gu, Liming Ding, Ju H. Park, Xiangpeng Xie
Abstract
This note proposes a novel weighted memory <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> controller for time-varying delayed Takagi–Sugeno fuzzy systems via a distributed delay method. In contrast to the traditional memory controller based on instantaneous historical data, the continuous historical information over a given period is utilized to construct the fuzzy-based memory controller, in which a weighting function is employed for the first time to describe the importance of historical information. Then, the weighted historical information is expressed as a distributed delay and the weights are represented as delay kernel. By using a less conservative integral inequality with respect to the weighted historical information, original sufficient conditions are deduced to solve the fuzzy weighted memory <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> controller gains. Finally, simulations are carried out to reveal the merits of the presented controller.