Weighted Memory H∞ Stabilization of Time-Varying Delayed Takagi–Sugeno Fuzzy Systems

This note proposes a novel weighted memory
$H_\infty$
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
$H_\infty$
controller gains. Finally, simulations are carried out to reveal the merits of the presented controller.