Synchronization of the hyperchaotic Lü systems using a sliding mode controller

This paper deals with the synchronization of two identical hyperchaotic master and slave systems. The slave system is assumed to have two inputs. A sliding mode controller is proposed to synchronize the two systems. Using Lyapunov theory, it is shown that the errors between the states of the master and slave systems asymptotically converge to zero when noise is not present in the systems. Moreover, in the presence of noise, the errors are shown to be bounded. Simulation results are presented to illustrate and reinforce the ability of the controller to synchronize the hyperchaotic systems. In addition, the proposed controller scheme is applied to the secure communication field where computer simulation results are provided to show the efficiency of the proposed controller.