zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.
93D15Stabilization of systems by feedback
37D45Strange attractors, chaotic dynamics
93C23Systems governed by functional-differential equations
[1]Pecora, L., Carrol, T.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990) · doi:10.1103/PhysRevLett.64.821
[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 · doi:10.1016/j.physleta.2007.06.020
[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)
[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 · doi:10.1016/j.physleta.2004.07.024
[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 · doi:10.1016/j.chaos.2004.04.024
[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)
[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) · doi:10.1142/S021812740100295X
[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 · doi:10.1142/S0218127406016677
[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) · doi:10.1016/j.physleta.2006.06.068
[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 · doi:10.1016/j.cnsns.2008.06.018
[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 · doi:10.1016/j.chaos.2003.10.026
[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 · doi:10.1016/j.chaos.2004.02.004
[13]Feki, M.: An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons Fractals 18, 141–148 (2003) · Zbl 1048.93508 · doi:10.1016/S0960-0779(02)00585-4
[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 · doi:10.1016/j.physleta.2008.06.061
[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 · doi:10.1109/81.572346
[16]Hale, J., Lunel, S.M.V.: Introduction to Functional Differential Equations. Springer, New York (1993)
[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 · doi:10.1023/A:1021781602182
[18]Park, Ju H., Won, S.: Stability analysis for neutral delay-differential systems. J. Frankl. Inst. 337, 1–9 (2000) · Zbl 0992.34057 · doi:10.1016/S0016-0032(99)00040-X
[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) · doi:10.1109/TAC.2006.886495
[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) · doi:10.1109/TCSI.2007.904640
[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 · doi:10.1080/00207720802300370
[22]Kolmanovskii, V.B., Myshkis, A.: Applied Theory to Functional Differential Equations. Kluwer Academic, Boston (1992)
[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 · doi:10.1016/j.chaos.2007.01.057
[24]Kharitonov, V.L., Niculescu, S.-I.: On the stability of linear systems with uncertain delay. IEEE Trans. Autom. Control 48, 127–132 (2003) · doi:10.1109/TAC.2002.806665
[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) · doi:10.1049/ip-cta:20050294
[26]Boyd, S., Ghaoui, L.El., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)
[27]Li, T., Fei, S.-M., Zhang, K.-J.: Synchronization control of recurrent neural networks with distributed delays. Physica A 387, 982–996 (2008) · doi:10.1016/j.physa.2007.10.010
[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)
[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
[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) · doi:10.1109/TNN.2008.2006904
[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 · doi:10.1016/j.neunet.2008.09.002
[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 · doi:10.1016/j.amc.2008.05.091