Synchronization of the fractional-order chaotic Chua's system via sliding mode observer

In this paper, we present a secured data transmission system based on synchronization of two fractional-order chaotic systems. First, the chaotic behavior of the fractional-order Chua's system is analyzed by varying the order of derivative of the state variables. Next, a step-by-step sliding mode observer is proposed to obtain robust synchronization of two fractional-order Chua's systems. The finite time convergence of the estimation error is established. The efficiency of the proposed synchronization method and the performance of the secured transmission based on the inclusion of the message in the system dynamics are illustrated by numerical simulations.