Fuzzy resilient control for synchronizing chaotic systems with time-variant delay and external disturbance

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 Script capital H-infinity 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.