The aim of the chapter is twofold. First, a literature review on synchronization methods of fractional-order discrete-time systems is exposed. Second, a secure digital data communication based on synchronization of fractional-order discrete-time chaotic systems is proposed. Two synchronization methods based on observers are proposed to synchronize two fractional-order discrete-time chaotic systems. The first method concerns the impulsive synchronization where sufficient conditions for the synchronization error of the states are given. The second method concerns the exact synchronization which is based on a step-by-step delayed observer. In the same way, conditions are provided in order to allow the reconstruction of the states and the unknown input which is the message in this case. The two synchronization methods are combined in order to design a novel robust secure digital data communication. The performance of the proposed communication system is illustrated in numerical simulations where digital image signal is considered.
Impulsive Synchronization of Fractional-Order Chaotic Systems With Actuator Saturation and Control Gain Error
