Exponential synchronization of chaotic systems subject to uncertainties in the control input

A sliding mode control technique is introduced for exponential synchronization of chaotic systems. These systems are described by a general form including matched and unmatched nonlinear functions. A new hitting-free switching surface of proportional-integral type is proposed. This type of switching surface is without the hitting process if the attraction of sliding manifold is ensured. This property makes it easy to exponentially synchronize the master-slave chaotic systems. Based on this switching surface, a robust sliding mode controller (SMC) is derived to guarantee the attraction of sliding manifold even when the system is subjected to input uncertainties. An example is included to illustrate the results developed in this paper.