Secure communication based on chaotic synchronization via interval time-varying delay feedback control. (English) Zbl 1215.93127

Summary: A synchronization method of Lur’e systems for chaotic secure communication systems with interval time-varying delay feedback control is proposed. To increase communication security, the transmitted message is encrypted with the techniques of \(N\)-shift cipher and public key. Based on Lyapunov method and linear matrix inequality (LMI) formulation, new delay-dependent synchronization criteria are established to not only guarantee stable synchronization of both transmitter and receiver systems but also recover the transmitted original signal at the receiver. Throughout a numerical example, the validity and superiority of the proposed method are shown.


93D15 Stabilization of systems by feedback
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C23 Control/observation systems governed by functional-differential equations
Full Text: DOI


[1] Pecora, L., Carrol, T.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990) · Zbl 0938.37019
[2] Park, Ju H., Lee, S.M., Kwon, O.M.: Adaptive synchronization of Genesio–Tesi chaotic system via a novel feedback control. Phys. Lett. A 371, 263–270 (2007) · Zbl 1209.93122
[3] Park, Ju H.: Adaptive synchronization of a unified chaotic systems with an uncertain parameter. Int. J. Nonlinear Sci. Numer. Simul. 6, 201–206 (2005) · Zbl 1401.93123
[4] LU, J., Wu, X., Han, X., Lü, J.: Adaptive feedback synchronization of a unified chaotic system. Phys. Lett. A 329, 327–333 (2004) · Zbl 1209.93119
[5] Park, Ju H., Kwon, O.M.: LMI optimization approach to stabilization of time-delay chaotic systems. Chaos Solitons Fractals 23, 445–450 (2005) · Zbl 1061.93509
[6] Cao, J., Li, H.X., Ho, D.W.C.: Synchronization criteria of Lur’e systems with time-delay feedback control. Chaos Solitons Fractals 23, 1285–1298 (2005) · Zbl 1086.93050
[7] Yalçin, M.E., Suykens, J.A.K., Vandewalle, J.: Master–slave synchronization of Lur’e systems with time-delay. Int. J. Bifurc. Chaos 11, 1707–1722 (2001)
[8] He, Y., Wen, G., Wang, Q.-G.: Delay-dependent synchronization for Lur’e systems with delay feedback control. Int. J. Bifurc. Chaos 16, 3087–3091 (2001) · Zbl 1139.93349
[9] Xiang, J., Li, Y., Wei, W.: An improved condition for master–slave synchronization of Lur’e systems with time delay. Phys. Lett. A 362, 154–158 (2007)
[10] Li, T., Yu, J., Wang, Z.: Delay-range-dependent synchronization criterion for Lur’e systems with delay feedback control. Commun. Nonlinear Sci. Numer. Simul. 14, 1796–1803 (2009) () · Zbl 1221.93224
[11] Wang, C.C., Su, J.P.: A new adaptive variable structure control for chaotic synchronization and secure communication. Chaos Solitons Fractals 20, 967–977 (2004) · Zbl 1050.93036
[12] Yau, H.T.: Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos Solitons Fractals 22, 341–347 (2004) · Zbl 1060.93536
[13] Feki, M.: An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons Fractals 18, 141–148 (2003) · Zbl 1048.93508
[14] Sun, Y., Cao, J., Feng, G.: An adaptive chaotic secure communication scheme with channel noises. Phys. Lett. A 372, 5442–5447 (2008) · Zbl 1223.94023
[15] Yang, T., Wu, C.W., Chua, L.O.: Cryptography based on chaotic systems. IEEE Trans. Circuits Syst. I 44, 469–472 (1997) · Zbl 0884.94021
[16] Hale, J., Lunel, S.M.V.: Introduction to Functional Differential Equations. Springer, New York (1993) · Zbl 0787.34002
[17] Park, Ju H., Won, S.: Asymptotic stability of neutral systems with multiple delays. J. Optim. Theory Appl. 103, 183–200 (1999) · Zbl 0947.65088
[18] Park, Ju H., Won, S.: Stability analysis for neutral delay-differential systems. J. Frankl. Inst. 337, 1–9 (2000) · Zbl 0992.34057
[19] Xu, S., Lam, J.: On equivalence and efficiency of certain stability criteria for time-delay systems. IEEE Trans. Autom. Control 52, 95–101 (2007) · Zbl 1366.93451
[20] Xu, S., Lam, J., Mao, X.: Delay-dependent H control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Trans. Circuits Syst. I 54, 2070–2077 (2007) · Zbl 1374.93134
[21] Xu, S., Lam, J.: A survey of linear matrix inequality techniques in stability analysis of delay systems. Int. J. Syst. Sci. 39, 1095–1113 (2008) · Zbl 1156.93382
[22] Kolmanovskii, V.B., Myshkis, A.: Applied Theory to Functional Differential Equations. Kluwer Academic, Boston (1992) · Zbl 0917.34001
[23] Li, D., Wang, Z., Zhou, J., Fang, J., Ni, J.: A note on chaotic synchronization of time-delay secure communication systems. Chaos Solitons Fractals 38, 1217–1224 (2008) · Zbl 1152.93449
[24] Kharitonov, V.L., Niculescu, S.-I.: On the stability of linear systems with uncertain delay. IEEE Trans. Autom. Control 48, 127–132 (2003) · Zbl 1364.34102
[25] Yue, D., Peng, C., Tang, G.Y.: Guaranteed cost control of linear systems over networks with state and input quantisations. IEE Proc. Contr. Appl. 153, 658–664 (2006)
[26] Boyd, S., Ghaoui, L.El., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994) · Zbl 0816.93004
[27] Li, T., Fei, S.-M., Zhang, K.-J.: Synchronization control of recurrent neural networks with distributed delays. Physica A 387, 982–996 (2008)
[28] Zhang, Q., Wei, X., Xu, J.: Delay-dependent exponential stability of cellular neural networks with time-varying delays. Chaos Solitons Fractals 23, 1363–1369 (2005) · Zbl 1094.34055
[29] Gu, K.: An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE Conference on Decision and Control, December, Sydney, Australia (2000) p. 2805
[30] Gu, K.: Discretized Lyapunov functional for uncertain systems with multiple time-delay. In: Proceedings of 38th IEEE Conference on Decision and Control, December , Phoenix, A (1999) p. 2029 · Zbl 0959.93053
[31] Chen, W.-H., Zheng, W.X.: Improved delay-dependent asymptotic stability criteria for delayed neural networks. IEEE Trans. Neural Netw. 19, 2154–2161 (2008)
[32] Hu, L., Gao, H., Zheng, W.X.: Novel stability of cellular neural networks with interval time-varying delay. Neural Netw. 21, 1458–1463 (2008) · Zbl 1254.34102
[33] Kwon, O.M., Park, Ju H.: Exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays. Appl. Math. Comput. 203, 813–823 (2008) · Zbl 1170.34052
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