Robust synchronization of chaotic systems subject to parameter uncertainties

The robust synchronization problem is studied in this paper for uncertain chaotic Lur'e systems. It is assumed that the mismatched parameter uncertainties appear in the master system and are norm bounded. An integral sliding mode control approach is developed to address this problem. First, a suitable integral sliding surface is constructed, and a delay-dependent condition by means of linear matrix inequalities is derived under which the resulting error system is globally asymptotically stable in the specified switching surface. Then, an integral sliding mode controller is designed guaranteeing the reachability of the specified sliding surface. When the bounds of the mismatched parameter uncertainties are unknown, an adaptive integral sliding mode controller is further designed. Finally, the Chua's circuit is provided as an example to demonstrate the effectiveness of the developed approach.