Backstepping Design in Synchronizing Nonlinear Systems

Backstepping design is a recursive procedure that combines the choice of a Lyapunov function with the design of feedback control. In this paper, a practical backstepping design scheme is proposed for synchronizing nonlinear systems. In the scheme, only one feedback control is required regardless of the order of the system. It can be applied not only to ordinary nonlinear systems, but also to a variety of chaotic systems, such as van der Pol system and Duffing system with external excitation, Chua s circuit and system,etc. It is easy to be carried out since its feedback control has no derivatives. Examples of van der Pol system and Chua s circuit designs are presented.