A second-order sliding mode (SOSM) controller is proposed to synchronize a class of incommensurate fractional-order chaotic systems with model uncertainties and external disturbances. Based on the chattering free SOSM control scheme, it can be rigorously proved that the dynamics of the synchronization error is globally asymptotically stable by using the Lyapunov stability theorem. Finally, numerical examples are provided to illustrate the effectiveness of the proposed controller design approach.
"Robust Synchronization of Incommensurate Fractional-Order Chaotic Systems via Second-Order Sliding Mode Technique." J. Appl. Math. 2013 1 - 11, 2013. https://doi.org/10.1155/2013/321253