Complete synchronization of commensurate fractional order chaotic systems using sliding mode control

In this manuscript, we consider a new fractional order chaotic system which exhibits interesting behavior such as two, three, and four scrolls. Such systems can be found extensively in mechatronics and power electronic systems which exhibit self-sustained oscillations. Synchronization between two such systems is an interesting problem either theoretically or practically. Using a sliding mode control methodology, we synchronize a unidirectional coupling structure for the two chaotic systems. Numerical simulations are used to verify the theoretical analysis. Additionally, we report the robustness of the system in the presence of a noise in simulation.

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• Proposing a sliding mode control technique that guarantees the asymptotical stability of the error dynamics.
• Numerical simulations were used to show the effectiveness of the proposed control laws.
• Introducing a new fractional order chaotic system with various dynamical behaviors.