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

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 d...

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Bibliographic Details
Published in:International journal of applied mathematics and computer science 2019-03, Vol.29 (1), p.179-194
Main Authors: Djennoune, Said, Bettayeb, Maamar, Al-Saggaf, Ubaid Muhsen
Format: Article
Language:English
Subjects:
Chaos theory
chaotic map
chaotic synchronization
Communication
Computer simulation
dead-beat observer
Discrete time systems
fractional-order discrete time systems
Nonlinear systems
Observability (systems)
secure data communication
Synchronism
Time synchronization
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Summary: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.
ISSN:2083-8492
1641-876X
2083-8492
DOI:10.2478/amcs-2019-0014