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For the chaotic systems with disturbance, a sampled-data controller is designed to achieve chaotic synchronization. Firstly, to handle the discontinuity introduced by the sampling activities, the input-delay approach is introduced to transform the discontinuous chaotic systems into continuous ones. Secondly, the worst possible case of performance is considered according to min-max robust strategy. Then the sufficient conditions for global asymptotic synchronization of such chaotic systems are derived and expressed in terms of linear matrix inequality (LMI). The proposed algorithm can achieve synchronization of the sampled-data chaotic systems for all admissible disturbances at the pre-computed set of disturbance realizations. The effectiveness is finally illustrated via numerical simulations of chaotic Chuas circuit, and the simulation results show that the proposed algorithm is suitable for secure communication.
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Keywords:
- chaotic synchronization /
- sampled-data control /
- min-max /
- input-delay
[1] Aziz-Alaoui M A 2005 Proceeding of the IEEE Conference on Electronics, Circuits and Systems Gammarth, Tunisia, December 11-14, 2005 p1
[2] Ji Y, Wen C Y, Li Z G 2008 Int. J. Comm. Sys. 21 1137
[3] Li J F, Li N 2002 Chin. Phys. 11 1124
[4] Hu M F, Xu Z Y 2007 Chin. Phys. 16 3231
[5] Wang X Y, Wu X J, He Y J, Aniwar G 2008 Int. J. Modern Physics B 22 3709
[6] Lee S M, Choi S J, Ji D H, Park J H, Won S C 2010 Nonlinear Dynam 59 277
[7] Kwon O M, Park J H, Lee S M 2011 Nonlinear Dynam 63 239
[8] Ma T D, Jiang W B, Fu J, Chai Y, Chen L P, Xue F Z 2012 Acta Phys. Sin. 61 160506 (in Chinese) [马铁东, 江伟波, 浮洁, 柴毅, 陈立平, 薛方正 2012 物理学报 61 160506]
[9] Fu J, Yu M, Ma T D 2011 Chin. Phys. B 20 12508
[10] Ma T D, Jiang W B, Fu J 2012 Acta Phys. Sin. 61 090503 (in Chinese) [马铁东, 江伟波, 浮洁 2012 物理学报 61 090503]
[11] Lee S H, Kapila V, Porfiri M, Panda A 2010 Commun. Nonlinear Sci. Numer. Simulat 15 4100
[12] Lee S H, Kapila V, Porfiri M 2008 Proceedings of the American Control Conference Seattle, WA, USA, Jun 11-13, 2008 p523
[13] Barajas-Ramirez J G, Chen G, Shieh L S 2003 Int. J. Bifurc. Chaos 13 1197
[14] Barajas-Ramirez J G, Chen G, Shieh L S 2004 Int. J. Bifurc. Chaos 14 2721
[15] Barajas-Ramirez J G, Chen G, Shieh L S 2003 Proceedings of IEEE International Symposium on Intelligent Control Houston Texas, USA, October 5-8, 2003 p241
[16] Lam H K, Seneviratne L D 2008 IEEE Trans. Circuits Syst. I 55 883
[17] Zhang C K, He Y, Wu M 2009 IEEE Trans. Circuits Syst. II 56 320
[18] Lu J G, Hill D J 2008 IEEE Trans. Circuits Syst. II 55 586
[19] Zhu X L, Wang Y Y, Yang H Y 2010 Proceedings of the American Control Conference Baltimore, MD, USA, June 30-July 02, 2010 p1817
[20] Chen W H, Wang Z P, Lu X M 2012 IEEE Trans. Circuits Syst. II 59 515
[21] Feng Y F, Zhang Q L 2011 Chin. Phys. B 20 1
[22] Theesar S J S, Banerjee S, Balasubramaniam P 2012 Nonlinear Dynam 70 1977
[23] Ma D Z, Zhang H G, Wang Z S, Feng J 2010 Chin. Phys. B 19 0505061
[24] Lee T H, Park J H, Lee S M, Kwon O M 2013 Int. J. Control 86 107
[25] Fridman E, Shaked U, Suplin V 2007 Automatica 43 1072
[26] Fridman E, Shaked U, Suplin V 2007 Syst. Control Lett. 54 271
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[1] Aziz-Alaoui M A 2005 Proceeding of the IEEE Conference on Electronics, Circuits and Systems Gammarth, Tunisia, December 11-14, 2005 p1
[2] Ji Y, Wen C Y, Li Z G 2008 Int. J. Comm. Sys. 21 1137
[3] Li J F, Li N 2002 Chin. Phys. 11 1124
[4] Hu M F, Xu Z Y 2007 Chin. Phys. 16 3231
[5] Wang X Y, Wu X J, He Y J, Aniwar G 2008 Int. J. Modern Physics B 22 3709
[6] Lee S M, Choi S J, Ji D H, Park J H, Won S C 2010 Nonlinear Dynam 59 277
[7] Kwon O M, Park J H, Lee S M 2011 Nonlinear Dynam 63 239
[8] Ma T D, Jiang W B, Fu J, Chai Y, Chen L P, Xue F Z 2012 Acta Phys. Sin. 61 160506 (in Chinese) [马铁东, 江伟波, 浮洁, 柴毅, 陈立平, 薛方正 2012 物理学报 61 160506]
[9] Fu J, Yu M, Ma T D 2011 Chin. Phys. B 20 12508
[10] Ma T D, Jiang W B, Fu J 2012 Acta Phys. Sin. 61 090503 (in Chinese) [马铁东, 江伟波, 浮洁 2012 物理学报 61 090503]
[11] Lee S H, Kapila V, Porfiri M, Panda A 2010 Commun. Nonlinear Sci. Numer. Simulat 15 4100
[12] Lee S H, Kapila V, Porfiri M 2008 Proceedings of the American Control Conference Seattle, WA, USA, Jun 11-13, 2008 p523
[13] Barajas-Ramirez J G, Chen G, Shieh L S 2003 Int. J. Bifurc. Chaos 13 1197
[14] Barajas-Ramirez J G, Chen G, Shieh L S 2004 Int. J. Bifurc. Chaos 14 2721
[15] Barajas-Ramirez J G, Chen G, Shieh L S 2003 Proceedings of IEEE International Symposium on Intelligent Control Houston Texas, USA, October 5-8, 2003 p241
[16] Lam H K, Seneviratne L D 2008 IEEE Trans. Circuits Syst. I 55 883
[17] Zhang C K, He Y, Wu M 2009 IEEE Trans. Circuits Syst. II 56 320
[18] Lu J G, Hill D J 2008 IEEE Trans. Circuits Syst. II 55 586
[19] Zhu X L, Wang Y Y, Yang H Y 2010 Proceedings of the American Control Conference Baltimore, MD, USA, June 30-July 02, 2010 p1817
[20] Chen W H, Wang Z P, Lu X M 2012 IEEE Trans. Circuits Syst. II 59 515
[21] Feng Y F, Zhang Q L 2011 Chin. Phys. B 20 1
[22] Theesar S J S, Banerjee S, Balasubramaniam P 2012 Nonlinear Dynam 70 1977
[23] Ma D Z, Zhang H G, Wang Z S, Feng J 2010 Chin. Phys. B 19 0505061
[24] Lee T H, Park J H, Lee S M, Kwon O M 2013 Int. J. Control 86 107
[25] Fridman E, Shaked U, Suplin V 2007 Automatica 43 1072
[26] Fridman E, Shaked U, Suplin V 2007 Syst. Control Lett. 54 271
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