This paper addresses the transient performance of nonlinear systems described by Takagi‐Sugeno (TS) fuzzy models. To achieve this goal, a modified fuzzy controller and a non‐quadratic Lyapunov function (NQLF) are utilized. The fuzzy controller comprises an α‐delayed non‐parallel distributed compensation (non‐PDC) and a nonlinear modifying term. The α‐delayed non‐PDC assures the global stabilization of the TS fuzzy systems through the NQLF and linear matrix inequality (LMI) numerical technique. Moreover, the modifying term is used to enhance the transient performance. It is shown that the stability of the closed‐loop system is guaranteed by the α‐delayed non‐PDC and the performance is improved by the modifying term. Two different selections for the modifying term are presented and that they can increase the reaching time of the response and lead to the finite‐time convergence of the state to their equilibrium point is proven. Several numerical and practical systems, that is, a single‐link manipulator and a chaotic permanent magnet synchronous machine, are simulated to illustrate the advantages of the proposed approach. The obtained numerical results are compared with other state‐of‐the‐art methods.

中文翻译：

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改进的非并行分布补偿控制器改善高木-杉野模糊系统的暂态性能

本文讨论了由Takagi-Sugeno（TS）模糊模型描述的非线性系统的暂态性能。为了实现这个目标，使用了改进的模糊控制器和非二次李雅普诺夫函数（NQLF）。模糊控制器包括一个α延迟非平行分布补偿（non-PDC）和一个非线性修正项。通过NQLF和线性矩阵不等式（LMI）数值技术，α延迟的非PDC保证了TS模糊系统的全局稳定性。此外，修改项用于增强瞬态性能。结果表明，α保证了闭环系统的稳定性。延迟的非PDC，并且通过修改项可以提高性能。提出了两个不同的修改项选择，它们可以增加响应的到达时间并导致状态到其平衡点的有限时间收敛。仿真了一些数值和实际系统，即单链接机械手和混沌永磁同​​步电机，以说明该方法的优点。将获得的数值结果与其他最新方法进行比较。