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A NEW SYNCHRONIZATION PRINCIPLE FOR A CLASS OF LUR'E SYSTEMS WITH APPLICATIONS IN SECURE COMMUNICATION

INRIA Lorraine, Projet CONGE, I.S.G.M.P. Bât A, Ile de Saulcy, 57045 Metz, Cedex 01, France

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Laboratoire de Mécanique et de Méthodes Numériques, Faculté des Sciences, Université de Yaoundé I, B.P. 812 Yaoundé, Cameroun

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RODOUMTA KOINA

Faculté des Sciences Exactes et Appliquées, Université de Ndjamena, B.P. 1027 Ndjamena, Tchad

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https://doi.org/10.1142/S0218127404010758Cited by:31 (Source: Crossref)

Abstract

In this Letter, we propose a new synchronization principle for a class of Lur'e systems. We design, using only a single scalar output, a possible class of observers to detect whether two dynamical systems exhibit identical oscillations. The proposed method is then applied to suggest a means to secure communications. The transmitter contains a chaotic oscillator with an input that is modulated by the information signal. The receiver is a copy of the transmitter driven by a synchronization signal. The advantage of this method over the existing one is that the synchronization time is explicitly computed. An illustrative example of the cubic Chua's circuit is given to show the effectiveness of the proposed approach.

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References

T. L. Caroll and L. M. Pecora, IEEE Trans. Circuits Syst.-I 38, 453 (1991). Crossref, Web of Science, Google Scholar
Chen, G. [1997] "Control and synchronization of chaos, a bibliography," available FTP: uhoop.egr.uh.edu/pub/Tex/chaos.tex . Google Scholar
N. J. Corron and D. W. Hahs, IEEE Trans. Circuits Syst.-I 44, 373 (1997). Crossref, Web of Science, Google Scholar
N. J. Corron, Phys. Rev. E63, 055203 (2001). Google Scholar
K. M. Cuomo, A. V. Oppenheim and S. H. Strogatz, IEEE Trans. Circuits Syst.-I 40, 626 (1993). Crossref, Web of Science, Google Scholar
G. Grassi and S. Mascolo, IEEE Trans. Circuits Syst.-II 44, 1011 (1997). Crossref, Web of Science, Google Scholar
K. S. Halle, C. W. Wu and L. O. Chua, Int. J. Bifurcation and Chaos 3, 469 (1993). Link, Web of Science, Google Scholar
Hartley, T. T. [1989] "The Duffing double scroll," in Proc. American Control Conf., Pittsburgh, PA., pp. 1–7 . Google Scholar
M. Itoh, C. W. Wu and L. O. Chua, Int. J. Bifurcation and Chaos 7, 275 (1997). Link, Web of Science, Google Scholar
M. P. Kennedy, IEEE Trans. Circuits Syst.-I 41, 771 (1994). Crossref, Web of Science, Google Scholar
L. Kocarevet al., Int. J. Bifurcation and Chaos 2, 709 (1992). Link, Google Scholar
V. I. Korobov, Dokl. Acad. Nauk SSSR T.248, 1051 (1979). Google Scholar
V. I. Korobov, Mat. Sbornik T.109, 582 (1979). Google Scholar
J. P. LaSalle and S. Letschetz , Stability by Liapunov's Direct Method with Application ( Academic Press , NY , 1961 ) . Google Scholar
H. Leung and J. Lam, IEEE Trans. Circuits Syst.-I 44, 262 (1997). Crossref, Web of Science, Google Scholar
T. L. Liao and N. Huang, IEEE Trans. Circuits Syst.-I 46, 1144 (1999). Crossref, Web of Science, Google Scholar
A. M. Liapunov, Traduction Française: Ann. Fac. Sci. Toulouse 9 (Reed. Princiton University Press, 1907) pp. 203–310. Google Scholar
R. N. Madan , Chua's Circuit: A Paradigm for Chaos ( World Scientific , Singapore , 1993 ) . Link, Google Scholar
Marinitch, A. P. & Rodoumta, K. [1986] "Sur la structure d'unefamille de fonction de controllabilité dans le probléme de synthèse de commandes bornées," "La méthode de fonctions de Liapunov dans les mathèmatiques contemporains," Acte du Colloque Scientifique 27–29 Mai, Kharkiv, pp. 65–76 . Google Scholar
O. Morgul and E. Solak, Phys. Rev. E54, 4803 (1996). Google Scholar
O. Morgul and E. Solak, Int. J. Bifurcation and Chaos 7, 1307 (1997). Link, Web of Science, Google Scholar
H. Nijmeiher and I. M. Mareels, IEEE Trans. Circuits Syst.-I 40, 882 (1997). Google Scholar
M. J. Ogorzalek, IEEE Trans. Circuits Syst.-I 40, 693 (1993). Crossref, Web of Science, Google Scholar
U. Parlitzet al., Int. J. Bifurcation and Chaos 2, 973 (1992). Link, Web of Science, Google Scholar
K. Pyragas, Phys. Rev. E58, 3067 (1998). Google Scholar
R. Rajamani and Y. Cho, Proc. 34th Conf. Decision Control (New Orleans, LA, 1995) pp. 93–94. Google Scholar
J. P. Ramirez, H. Puebla and I. Cervantes, Int. J. Bifurcation and Chaos 7, 1605 (2002). Google Scholar
G. Santoboni, Yu. A. Pogromsky and H. Nijmeiher, Phys. Lett. A291, 265 (2001). Google Scholar
K. M. Short, Int. J. Bifurcation and Chaos 4, 959 (1994). Link, Web of Science, Google Scholar
X. S. Yang, Int. J. Bifurcation and Chaos 12, 1159 (2002). Link, Web of Science, Google Scholar