Simple adaptive synchronization of chaotic systems with random components

Practical systems usually possess random components. Random components often affect the robustness of synchronism and must be taken into consideration in the design of synchronization. In the present study, we assume that the system satisfies the Lipschitz condition, and the random component is uniformly bounded. By the partial stability theory, we are able to prove that two simple adaptive variable structure controllers achieve synchronization of chaotic systems. Moreover, we discuss how the controllers can be modified to eliminate the undesired phenomenon of chattering. The Duffing two-well system and the Chua circuit system are simulated to illustrate the theoretical analysis.