Synchronization of nonlinear systems with stair-step signal

From the viewpoint of computer control, the synchronization of nonlinear systems is investigated. The controlled synchronization problem with stair-step signal is presented. The synchronization error controlled by the stair-step signal is analyzed and it is proved with Lyapunov method that if the Euclid norm of the control signal is no more than the norm of the synchronization error times a constant, and the signal makes the Euler approximate model of the error exponentially stable, then the stair-step signal will make the slave synchronized with the master.