Backstepping synchronization of chaotic system based on equivalent transfer function method

In order to solve the synchronization problem of chaotic systems with reduced number of active control inputs, special second order system was characterized and researched. A novel kind of equivalent transfer function method was integrated with backstepping method to solve the difficulty caused by double control coefficients of a kind of minimum phase second order system without uncertainties. And by constructing a Lyapunov function, the stability of the close loop system is proved. And also an additional stable condition for transfer function should be satisfied. At last, the proper chosen of control gain interval is calculated by an inequality equation, which is testified by detailed simulation to be very useful in the controller design. Also, detailed simulation on the synchronization of chaotic system was done the testify the rightness of the proposed method. (C) 2016 Elsevier GmbH. All rights reserved.