Synchronization of chaotic systems based on PI observer design

Synchronization problem of chaotic systems via observer method is investigated. In contrast to the results of the literatures, we consider the case that there exist noise disturbances in the output. Under this condition, it is not ideal to employ the classic observer to solve the synchronization problem. The proportional integral observer is proposed, which can render the error system stable with the noise in the output. Simulations on synchronizing Chua chaotic systems are done to verify the effectiveness of the main results.