Chaos synchronization using single variable feedback based on backstepping method

In recent years, backstepping method has been developed in the field of nonlinear control, such as controller, observer and output regulation. In this paper, an effective backstepping design is applied to chaos synchronization. There are some advantages in this method for synchronizing chaotic systems, such as (a) the synchronization error is exponential convergent; (b) only one variable information of the master system is needed; (c) it presents a systematic procedure for selecting a proper controller. Numerical simulations for the Chuaʹs circuit and the Rössler system demonstrate that this method is very effective.