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\(\mathcal{H}_{\infty}\) synchronization of chaotic systems via dynamic feedback approach. (English) Zbl 1221.93087
Phys. Lett., A 372, No. 29, 4905-4912 (2008); erratum ibid. 374, No. 17-18, 1900 (2010).
Summary: This Letter considers \(\mathcal{H}_{\infty}\) synchronization of a general class of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an \(\mathcal{H}_{\infty}\) norm constraint. A dynamic feedback control scheme is proposed for \(\mathcal{H}_{\infty}\) synchronization in chaotic systems for the first time. Then, a criterion for existence of the controller is given in terms of LMIs. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme.

93B52 Feedback control
34D06 Synchronization of solutions to ordinary differential equations
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
Full Text: DOI DOI
[1] Fujisaka, H.; Yamada, T., Prog. theor. phys., 69, 32, (1983)
[2] Pecora, L.M.; Carroll, T.L., Phys. rev. lett., 64, 821, (1990)
[3] Das, P.K.; Schieve, W.C.; Zeng, Z., Phys. lett. A, 161, 60, (1991)
[4] Chen, G.; Dong, X., From chaos to order: methodologies, perspectives and applications, (1998), World Scientific Singapore
[5] Ott, E.; Grebogi, C.; Yorke, J.A., Phys. rev. lett., 64, 1196, (1990)
[6] Wang, C.C.; Su, J.P., Chaos solitons fractals, 20, 967, (2004)
[7] Yau, H.T., Chaos solitons fractals, 22, 341, (2004)
[8] Yang, X.S.; Chen, G., Chaos solitons fractals, 13, 1303, (2002)
[9] Park, J.H.; Kwon, O.M., Chaos solitons fractals, 23, 445, (2005)
[10] Wu, X.; Lu, J., Chaos solitons fractals, 18, 721, (2003)
[11] Vincent, U.E., Phys. lett. A, 343, 133, (2005)
[12] Park, J.H.; Lee, S.M.; Kwon, O.M., Phys. lett. A, 371, 263, (2007)
[13] Park, J.H., Int. J. nonlinear sci. numer. simul., 6, 201, (2005)
[14] Park, J.H., Chaos solitons fractals, 27, 1279, (2006)
[15] Park, J.H., Chaos solitons fractals, 25, 579, (2005)
[16] Park, J.H., Chaos solitons fractals, 23, 1319, (2005)
[17] Park, J.H.; Lee, S.M.; Kwon, O.M., Chaos solitons fractals, 30, 271, (2007)
[18] Hou, Y.-Y.; Liao, T.-L.; Yan, J.-J., Physica A, 379, 81, (2007)
[19] Anton, S., The \(\mathcal{H}_\infty\) control problem, (1992), Prentice Hall New York
[20] Zhang, L.; Huang, B.; Lam, J., IEEE trans. circuits syst., 50, 615, (2003)
[21] Boyd, S.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004
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