An answer to the open problem of $mathcal{L}_2 - mathcal{L}_infty$ synchronization for time-delayed chaotic systems

摘要

In this paper, we deal with the open problem of $mathcal{L}_2 - mathcal{L}_infty$ synchronization for time-delayed chaotic systems with external disturbance. To date, a control scheme has been proposed to synchronize chaotic systems without time delay, but no solution exists for the case when chaotic systems have time delay. For the first time, in this paper, we prove that a new criterion for the $mathcal{L}_2 - mathcal{L}_infty$ synchronization of time-delayed chaotic systems exists.