Synchronization of Chaotic Systems in the Presence of Noise

Recently, a lot of efforts have been devoted to the synchronization of chaotic systems for chaotic secure communication. However, all the results on perfect synchronization are obtained under the ideal condition that the chaotic systems in both the transmitter side and the receiver side are noise free. In this paper, we relax this condition by designing a controller for the driven system based on the bounds of the system noise. Perfect synchronization of the two systems is theoretically established. Numerical results also illustrate the robustness and effectiveness of the proposed scheme