Discrete fractional order chaotic systems synchronization based on the variable structure control with a new discrete reaching-law

In this paper, we directly derive a new discrete state space expression of the fractional order chaotic system based on the fractional order Grnwald-Letnikow (G-L) definition and design a variable structure controller with a new faster reaching-law. The new reaching-law has the advantages of weakening the high frequency shake. Firstly, the condition of the discrete sliding mode surface is demonstrated. Then a multi-parametric function for sliding mode surface is constructed for weakening the high frequency shake through improving the Gao discrete reaching-law. Finally, the newly designed variable structure controller is applied to realize the synchronization of two different order discrete fractional chaotic systems. The simulation results show that the designed controller in this paper is effective, as it can achieve the synchronization of the discrete fractional order chaotic systems with external disturbances. Theoretical analysis and simulation results prove the effectiveness and robustness of this control method.