This paper focuses on the issue of fuzzy resilient control for synchronizing chaotic systems with time-variant delay and external disturbance. The goal is to design a fuzzy resilient controller with additive gain perturbations to guarantee that not only the drive and response systems are asymptotically synchronized in the absence of external disturbance, but also the synchronization error system has a prescribed disturbance attenuation index under the zero initial condition. By utilizing an appropriate Lyapunov–Krasovskii functional, the Bessel–Legendre inequality, and the reciprocally convex combination technique, a criterion on the stability and ℋ∞ performance of the synchronization error system is derived. Then, by means of some decoupling methods, a design scheme of the fuzzy resilient controller is developed. Finally, one numerical example is provided to examine the effectiveness of the fuzzy resilient controller design scheme.

中文翻译：

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用于同步具有时变延迟和外部干扰的混沌系统的模糊弹性控制

本文重点研究了具有时变延迟和外部干扰的混沌系统的同步模糊弹性控制问题。目标是设计一个具有加性增益扰动的模糊弹性控制器，以保证驱动和响应系统不仅在没有外部干扰的情况下渐近同步，而且同步误差系统在零初始条件下具有规定的干扰衰减指数. 通过利用适当的 Lyapunov-Krasovskii 泛函、Bessel-Legendre 不等式和倒数凸组合技术，一个关于稳定性和ℋ∞推导出同步误差系统的性能。然后，通过一些解耦方法，开发了模糊弹性控制器的设计方案。最后，提供了一个数值例子来检验模糊弹性控制器设计方案的有效性。