This paper comes up with an novel augmented Lyapunov–Krasovskii functional (LKF) approach to process finite-time passivity-based $H_{\infty }$ non-fragile state feedback control issue of Takagi–Sugeno fuzzy system (TSFS) via taking the effects of both time-varying delays and actuator faults. Designing a non-fragile controller to guarantee that TSFS is finite-time bounded (FTB) and meet finite-time mixed $H_{\infty }$ and passive performance is the focus of this paper. On the basis of the new augmented LKF and improved boundary techniques, sufficient delay-dependent conditions are inferred to acquire the desired results of the TSFS. Furthermore, the derived finite-time stability conditions are derived in terms of linear matrix inequalities (LMIs) and the controller gain matrices are confirmed through solving LMIs. Subsequently, three examples are addressed to certify the applicability and advantage of the put forward methodology.

本文提出了一种新的增强 Lyapunov-Krasovskii 泛函 (LKF) 方法来处理基于有限时间无源性的$H_{\infty }$Takagi-Sugeno 模糊系统 (TSFS) 的非脆弱状态反馈控制问题通过考虑时变延迟和执行器故障的影响。设计一个非脆弱控制器以保证 TSFS 是有限时间有界（FTB）并满足有限时间混合$H_{\infty }$被动性能是本文的重点。在新的增强 LKF 和改进的边界技术的基础上，推断出足够的延迟相关条件以获得 TSFS 的预期结果。此外，导出的有限时间稳定性条件是根据线性矩阵不等式 (LMI) 导出的，并且控制器增益矩阵通过求解 LMI 得到确认。随后，提出了三个例子来证明所提出的方法的适用性和优势。