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Synchronization of fractional-order discrete-time chaotic systems by an exact delayed state reconstructor: Application to secure communication

Djennoune Said, Bettayeb Maamar, Al-Saggaf Ubaid Muhsen

International Journal of Applied Mathematics and Computer Science

2019

Vol. 29, no. 1

179--194

This paper deals with the synchronization of fractional-order chaotic discrete-time systems. First, some new concepts regarding the output-memory observability of non-linear fractional-order discrete-time systems are developed. A rank criterion for output-memory observability is derived. Second, a dead-beat observer which recovers exactly the true state system from the knowledge of a finite number of delayed inputs and delayed outputs is proposed. The case of the presence of an unknown input is also studied. Third, secure data communication based on a generalized fractional-order Hénon map is proposed. Numerical simulations and application to secure speech communication are presented to show the efficiency of the proposed approach.