On observer synchronization of non-identical discrete-time hyperchaotic maps based on aggregation techniques and arrow form matrix

Rania Linda Filali, Mohamed Benrejeb, Pierre Borne


In this paper, new sufficient conditions for synchronization of non-identical discrete-time hyperchaotic maps is proposed for hyperchaotic cryptosystem communication.
They use aggregation techniques for stability study associated to the Benrejeb arrow form matrix for system description. In addition, suitable choice of
outputs feedback brings the problem of synchronization of two non-identical hyperchaotic maps to two identical hyperchaotic maps one. The considered case of
synchronization of third order hyperchaotic Hénon-Baier Klein maps shows the efficiency of the proposed approach to recover secure transmission of an image and a


synchronization; discrete-time hyperchaotic maps; aggregation technique; arrow form matrix; secure communication

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Pecora, L.M.; Carrol, l, T.L. (1990); Synchronization in chaotic systems, Phys. Rev. Lett., 64(8) : 821-824.

Yan, Z. (2006); Q-S (complete or anticipated) synchronization backstepping scheme in a class of discrete-time chaotic (hyperchaotic) systems: A symbolic-numeric computation approach, An Interdisciplinary Journal of Nonlinear Science, ID 013119, 16(1).

Fotsin, H.B.; Daafouz, J.(2004); Adaptive synchronization of uncertain chaotic Colpitts oscillators based on parameter identification, Physics Letters, Section A: General, Atomic and Solid State Physics, 339(3-5):304-315.

Park, J.H.(2006); Synchronization of Genesio chaotic system via backstepping approach, Chaos, Solitons and Fractals,27(5): 967-977.

Yassen, M.T.(2005); Chaos synchronization between two different chaotic systems using active control, Chaos, Solitons and Fractals, 23(12) : 131-140.

Borne, P.; Benrejeb, M.(2008); On the representation and the stability study of large scale systems, International Journal of Computers Communications & Control, 3(5): 55-66.

Borne, P.(1987); Non linear systems stability: vector norm approach, Systems and Control Encyclopedia, Pergamon Press, T.5: 3402-3406.

Borne, P.; Gentina, J.C.; Laurent,F.(1976); Stability study of large scale non linear discrete systems by use of vector norms, IFAC Symposium on Large Scale Systems Theory and Applications Udine: 187-193.

Benrejeb, M.(2010); Stability Study of Two Level Hierarchical Nonlinear Systems, Plenary lecture, 12th IFAC Large Scale Systems Symposium: Theory and Applications, IFAC-LSS, Lille.

Benrejeb, M.; Hammami, S.(2008); New approach of stabilization of nonlinear continuous monovariable processes characterized by an arrow form matrix, First International Conference, Systems ENgineering Design and Applications, SENDA, Monastir.

Benrejeb, M.; Soudani, D.; Sakly, A.; Borne, P.(2006); New discrete Tanaka Sugeno Kang fuzzy systems characterization and stability domain, International Journal of Computers Communications & Control, 1(4): 9-19.

Hammami, S.; Ben Saad, K.; Benrejeb, M.(2009); On the synchronization of identical and non-identical 4-D chaotic systems using arrow form matrix, Chaos, Solitons & Fractals, 42(1): 101-112.

On the synchronization of identical and non-identical 4-D chaotic systems using arrow form matrix, Chaos, Solitons & Fractals, 42(1): 101-112.

Filali, R.L.; Benrejeb, M.; Borne, P.(2014); On observer-based secure communication design using discrete-time hyperchaotic systems, Commun. Nonlinear Sci. Numer. Simulat., 9(5): 1424-1432.

Filali, R.L.; Hammami, S.; Benrejeb, M.; Borne, P.(2012); On Synchronization, Antisynchronization and Hybrid Synchronization of 3D Discrete Generalized Hénon Map, Nonlinear Dynamics and Systems Theory, 12(1): 81-95.

Filali, R.L.; Hammami, S.; Benrejeb, M.; Borne, P.(2012); Synchronization of discrete-time hyperchaotic maps based on aggregation technique for encryption, Systems, Signals and Devices (SSD), 2012 9th International Multi-Conference, Chemnitz : 1-6.

Robert, F.(1964); Normes vectorielles de vecteurs et de matrices, RFTI Chiffres, 17(4): 61-299.

Baier, G.; Klein, M.(1990); Maximum hyperchaos in generalized Hénon circuit, Phys. Lett. A., 151(67): 281-284.

Jiang, G.P.; Tang, W.K.S.; Chen, G.(2003); A simple global synchronization criterion for coupled chaotic systems, Chaos, Solitons and Fractals, 15(5): 925-935.

Millerioux, G.; Daafouz, J.(2003); An Observer-Based Approach for Input-Independent Global Chaos Synchronization of Discrete-Time Switched Systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 50(10) : 1270-1279.

DOI: https://doi.org/10.15837/ijccc.2015.3.709

Copyright (c) 2017 Rania Linda Filali, Mohamed Benrejeb, Pierre Borne

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