A general method for chaos synchronization and parameters estimation between different systems

For two different chaotic systems, which have the drive system with unknown parameters and the response system with known parameters, a unified mathematical expression for the controller and adaptive laws of parameters is proposed to realize complete synchronization and parameters estimation. The suggested method proves to be globally and asymptotically stable by means of the invariance principle of differential equations and the control technique of partial system states. The synchronizations between Lorenz system and Liu system, hyperchaotic Chen system and hyperchaotic new system are taken as two illustrative examples to demonstrate the effectiveness of this method.