Synchronization of Unified Chaotic System by Robust H_∞/Sliding Mode Control

This paper investigates the chaos synchronization problem for a class of uncertain unified chaotic systems with external disturbances. Based on the proportional-integral (PI) switching surface, a sliding mode controller (SMC) is derived to not only guarantee the occurrence of a sliding motion of error states, but also reduce the effect of external disturbances to an H∞-norm performance. Also, a new reaching law is introduced to reduce the chattering problem that is produced by traditional sliding mode control. The parameters necessary for constructing both PI switching surface and the SMC can be found by the linear matrix inequality (LMI) optimization technique. Finally, a numerical simulation is presented to show the effectiveness of the proposed method.