Anti-synchronization for a class of multi-dimensional autonomous and non-autonomous chaotic systems on the basis of the sliding mode with noise

This paper focuses on anti-synchronization for a class of chaotic systems with noise on the basis of the sliding mode control strategy. In order to achieve this target, a proportional integral surface is proposed to simplify the task of assigning the performance of the error system in sliding motion. We use fewer control items but realize a globally and exponentially asymptotical anti-synchronization. Furthermore, three typical examples are presented: a three-dimensional (3D) autonomous chaotic system, a 4D autonomous chaotic system and a 5D non-autonomous chaotic system. Finally, simulation results are demonstrated for multi-dimensional chaotic systems to illustrate the effectiveness of the proposed scheme.