Lag synchronization based on nonlinear observer design for delay system

We introduce the concept of lag observer; based upon this idea we present an analytical treatment of lag synchronization in unidirectional coupled time delayed systems. It can give a unified treatment of lag synchronization for a rather wide class of delay systems to assure exact lag synchronization, and several important systems are considered as examples. It also preserves the usual advantages, that is: (1) it enables lag synchronization be achieved in a systematic way; (2) it does not require the computation of any Lyapunov exponent; (3) it does not require initial conditions belonging to the same basin of attraction.