Geodesic
Synchronization of fractional-order discrete-time chaotic systems by an exact delayed state reconstructor: Application to secure communication
International Journal of Applied Mathematics and Computer Science, Tome 29 (2019) no. 1, pp. 179-194.

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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.
Keywords: fractional order, discrete time system, chaotic map, chaotic synchronization, dead-beat observer, secure data communication
Mots-clés : rząd ułamkowy, układ dyskretny, synchronizacja chaosu, komunikacja bezpieczna 
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Djennoune, Said; Bettayeb, Maamar; Al-Saggaf, Ubaid Muhsen. Synchronization of fractional-order discrete-time chaotic systems by an exact delayed state reconstructor: Application to secure communication. International Journal of Applied Mathematics and Computer Science, Tome 29 (2019) no. 1, pp. 179-194. http://geodesic.mathdoc.fr/item/IJAMCS_2019_29_1_a13/

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