Souza, Fernando O.; Palhares, Reinaldo M.; Mendes, Eduardo M. A. M.; Torres, Leonardo A. B. Further results on master-slave synchronization of general Lur’e systems with time-varying delay. (English) Zbl 1146.93031 Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 1, 187-202 (2008). Summary: 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. Cited in 18 Documents MSC: 93D09 Robust stability 34D20 Stability of solutions to ordinary differential equations 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 93B52 Feedback control 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory Keywords:synchronization; Lur’e system; time-delay; robust stability; asymptotic and exponential stability PDFBibTeX XMLCite \textit{F. O. Souza} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 1, 187--202 (2008; Zbl 1146.93031) Full Text: DOI References: [1] DOI: 10.1142/S0218127406015970 · Zbl 1192.94088 · doi:10.1142/S0218127406015970 [2] DOI: 10.1023/B:AURC.0000023528.59389.09 · Zbl 1115.37315 · doi:10.1023/B:AURC.0000023528.59389.09 [3] Blakely J. N., Phys. Rev. Lett. 92 pp 193901-1– [4] DOI: 10.1109/3.817635 · doi:10.1109/3.817635 [5] DOI: 10.1143/PTP.69.32 · Zbl 1171.70306 · doi:10.1143/PTP.69.32 [6] DOI: 10.1142/S0218127406014800 · Zbl 1097.94004 · doi:10.1142/S0218127406014800 [7] DOI: 10.1016/j.physleta.2004.09.080 · Zbl 1123.94351 · doi:10.1016/j.physleta.2004.09.080 [8] DOI: 10.1142/S0218127403006455 · Zbl 1129.93509 · doi:10.1142/S0218127403006455 [9] DOI: 10.1109/TCSI.2001.972854 · doi:10.1109/TCSI.2001.972854 [10] DOI: 10.1049/ip-cta:20041225 · doi:10.1049/ip-cta:20041225 [11] DOI: 10.1016/j.camwa.2005.04.003 · Zbl 1093.93009 · doi:10.1016/j.camwa.2005.04.003 [12] DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821 [13] DOI: 10.1016/j.automatica.2004.03.004 · Zbl 1059.93108 · doi:10.1016/j.automatica.2004.03.004 [14] DOI: 10.1016/j.cam.2004.12.025 · Zbl 1097.34057 · doi:10.1016/j.cam.2004.12.025 [15] DOI: 10.1142/S021812740100295X · doi:10.1142/S021812740100295X This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.