Sliding mode synchronization of second order chaotic subsystem based on equivalent transfer function method

Abstract

A novel kind of synchronization with reduced number of active inputs is very valuable since this kind of synchronization is more difficult to be deciphered in secure communication. The synchronization problem was first transferred to be a control problem of a special kind of second order system. To solve the high order derivative of control law problem caused by double control coefficients of a kind of second order system, a kind of novel equivalent transfer function method was integrated with common sliding mode method. And the system stability was proved by constructing a Lyapunov function. Furthermore, to make the system stable, also the condition for the stability of transfer function was proposed. What is more important is that the non-mini-phase situation was considered and corresponding method was proposed to solve its control problem. And at last, detailed simulation were done for both second order systems and synchronization of chaotic systems to show the rightness and effectiveness of the proposed method.