Robust $${H_\infty }$$H∞ synchronization of chaotic systems with unmatched disturbance and time-delay

This paper deals with master-slave robust $${H_\infty }$$H∞ synchronization of identical chaotic systems with the disturbance and time-delay via state feedback control, but the uncertain disturbance of the slave system is different from the master system. The sufficient conditions for achieving synchronization of two chaotic systems are derived on the basis of the Lyapunov theory and the linear matrix inequality technique, which is not only to guarantee the asymptotic synchronization but also to attenuate the effects of the perturbation on the overall error system to a prescribed level. Finally, an illustrative numerical simulation is also given to demonstrate the effectiveness of the proposed scheme.