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FURTHER RESULTS ON MASTER-SLAVE SYNCHRONIZATION OF GENERAL LUR'E SYSTEMS WITH TIME-VARYING DELAY

Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil

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REINALDO M. PALHARES

Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil

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EDUARDO M. A. M. MENDES

Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil

Author for correspondence.

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, and

LEONARDO A. B. TÔRRES

Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil

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https://doi.org/10.1142/S0218127408020227Cited by:31 (Source: Crossref)

Abstract

In this paper, a new approach to analyze the asymptotic, exponential and robust stability of the master-slave synchronization for Lur'e systems using time-varying delay feedback control is proposed. The discussion is motivated by the problem of transmitting information in optical communication systems using chaotic lasers. The approach is based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz–Newton model based transformation, without including any additional dynamics. Using the problem of synchronizing coupled Chua's circuits, three examples are given to illustrate the effectiveness of the proposed methodology.

Keywords:

References

G. Alvarez and S. Li, Int. J. Bifurcation and Chaos 16, 2129 (2006). Link, Web of Science, Google Scholar
B. R. Andrievskii and A. L. Fradkov, Autom. Rem. Contr. 65, 505 (2004), DOI: 10.1023/B:AURC.0000023528.59389.09. Crossref, Web of Science, Google Scholar
J. N. Blakely, L. Illing and D. J. Gauthier, Phys. Rev. Lett. 92, 193901-1 (2004), DOI: 10.1103/PhysRevLett.92.193901. Google Scholar
H. F. Chen and J. M. Liu, IEEE J. Quant. Electron. 36, 27 (2000), DOI: 10.1109/3.817635. Crossref, Web of Science, Google Scholar
H. Fujisaka and T. Yamada, Progr. Theoret. Phys. 69, 32 (1983), DOI: 10.1143/PTP.69.32. Crossref, Web of Science, Google Scholar
H. Huang, H.-X. Li and J. Zhong, Int. J. Bifurcation and Chaos 16, 281 (2006). Link, Web of Science, Google Scholar
C.-M. Kimet al., Phys. Lett. A 333, 235 (2004), DOI: 10.1016/j.physleta.2004.09.080. Crossref, Web of Science, Google Scholar
X. Liao and G. Chen, Int. J. Bifurcation and Chaos 13, 207 (2003). Link, Web of Science, Google Scholar
J. M. Liu, H. F. Chen and S. Tang, IEEE Trans. Circuits Syst.-I 48, 1475 (2001), DOI: 10.1109/TCSI.2001.972854. Crossref, Web of Science, Google Scholar
Niculescu, S. I. [1996] Sur la Stabilité et la Stabilisation des Systèmes Linéaires à États Retardés. PhD thesis, Institut National Polytechnique de Grenoble . Google Scholar
R. M. Palhareset al., IEE Proc. Contr. Th. Appl. 152, 27 (2005), DOI: 10.1049/ip-cta:20041225. Crossref, Google Scholar
R. M. Palhareset al., Comput. Math. Appl. 50, 13 (2005), DOI: 10.1016/j.camwa.2005.04.003. Crossref, Web of Science, Google Scholar
L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990), DOI: 10.1103/PhysRevLett.64.821. Crossref, Web of Science, Google Scholar
M. Wuet al., Automatica 40, 1435 (2004), DOI: 10.1016/j.automatica.2004.03.004. Crossref, Web of Science, Google Scholar
S. Xuet al., J. Comput. Appl. Math. 183, 16 (2005), DOI: 10.1016/j.cam.2004.12.025. Crossref, Web of Science, Google Scholar
M. E. Yalçin, J. A. K. Suykens and J. Vandewalle, Int. J. Bifurcation and Chaos 11, 1707 (2001). Link, Web of Science, Google Scholar