Synchronization of chaotic systems with uncertainty based on sliding mode control design

A chaotic synchronizing controller is provided based on the sliding mode control design. To make the controller physically realizable, available synchronizing error is used to estimate system uncertainty, such as the structure difference or parameter mismatching, based on the extended states observer (ESO), and then this controller is used to synchronizing two continuous chaotic systems. Illustrative example of the synchronization of Duffing and Vander Pol oscillators is given to show the effectiveness of this method.