Initial rectified attractors for perfect synchronization of chaotic systems

The controlled attractor with initial rectifying action, referred to as initial rectified attractor (IRA) in this Letter, is introduced for the purpose of chaos synchronization. An IRA-based design is presented to make the states of the drive system and the response system synchronized within finite time. The reaching time is shown independent of initial conditions and dynamics of the chaotic systems, and can be pre-specified. With numerical experiments we demonstrate that such perfect synchronization can be achieved for modified Chua's circuit systems and Genesio chaotic systems.