Abstract: Based on sliding mode control and proportional integral sliding mode control, the author designed sliding mode functions and controller, and gave sufficient conditions for synchronization of fractionalorder NewtonLeipnik chaotic systems. The results show that the masterslave systems of fractionalorder Newton Leipnik systems obtain sliding mode synchronization and proportional integral sliding mode synchronization if proper control law and sliding mode surfaces are selected.

Key words: fractionalorder, NewtonLeipnik system, chaos synchronization