Zhang, Liping; Jiang, Haibo; Bi, Qinsheng Reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems. (English) Zbl 1189.93085 Nonlinear Dyn. 59, No. 4, 529-534 (2010). Summary: The problem of reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems is investigated in this paper. Firstly a reliable impulsive controller is designed by the impulsive control theory. Then, some sufficient conditions for reliable impulsive lag synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method. Cited in 18 Documents MSC: 93C55 Discrete-time control/observation systems Keywords:chaotic systems; lag synchronization; impulsive synchronization; reliable control PDFBibTeX XMLCite \textit{L. Zhang} et al., Nonlinear Dyn. 59, No. 4, 529--534 (2010; Zbl 1189.93085) Full Text: DOI References: [1] Pecoral, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990) · Zbl 0938.37019 [2] Chen, G.R., Yu, X.H.: On time-delay feedback control of chaotic systems. IEEE Trans. Circuit Syst. I 64, 767–772 (1999) · Zbl 0951.93034 [3] Bainov, D.D., Simeonov, P.S.: Systems with Impulse Effect: Stability, Theory and Applications. Halsted Press, New York (1989) · Zbl 0676.34035 [4] Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989) · Zbl 0719.34002 [5] Yang, T.: Impulsive Control Theory. Springer, Berlin (2001) · Zbl 0996.93003 [6] Jiang, H.B., Yu, J.J., Zhou, C.G.: Robust fuzzy control of nonlinear fuzzy impulsive systems with time-varying delay. IET Control Theory Appl. 2, 654–661 (2008) [7] Yang, T., Yang, L.B., Yang, C.M.: Impulsive synchronization of Lorenz systems. Phys. Lett. A 226, 349–354 (1997) · Zbl 0773.35035 [8] Sun, J.T., Zhang, Y.P., Wu, Q.D.: Impulsive control for the stabilization and synchronization of Lorenz systems. Phys. Lett. A 298, 153–160 (2002) · Zbl 0995.37021 [9] Zhang, X.H., Liao, X.F., Li, C.D.: Impulsive control, complete and lag synchronization of unified chaotic system with continuous periodic switch. Chaos Solitons Fractals 26, 845–854 (2005) · Zbl 1093.93025 [10] Jiang, H.B.: Hybrid adaptive and impulsive synchronization of uncertain complex dynamical networks by the generalized Barbalat’s lemma. IET Control Theory Appl. (2009). doi: 10.1049/iet-cta.2008.0335 [11] Liu, B., Liu, X.Z.: Robust stability of uncertain discrete impulsive systems. IEEE Trans. Circuit Syst. II 54, 455–459 (2007) [12] Zhang, H., Guan, Z.H., Feng, G.: Reliable dissipative control for stochastic impulsive systems. Automatica 44, 1004–1010 (2008) · Zbl 1283.93258 [13] MacFarlane, A.G.J.: Complex Variable Methods for Linear Multivariable Feedback Systems. Taylor & Francis, London (1980) [14] Veillette, R.J., Medanic, J.V., Perkins, W.R.: Design of reliable control systems. IEEE Trans. Autom. Control 37, 290–304 (1992) · Zbl 0745.93025 [15] Chen, B., Liu, X.P.: Reliable control design of fuzzy dynamic systems with time-varying delay. Fuzzy Sets Syst. 146, 349–374 (2004) · Zbl 1055.93050 [16] Kuo, H.H., Hou, Y.Y., Yan, J.J., Liao, T.L.: Reliable synchronization of nonlinear chaotic systems. Math. Comput. Simul. 79, 1627–1635 (2009) · Zbl 1167.93016 [17] Zhang, Y., Sun, J.: Impulsive robust fault-tolerant feedback control for chaotic Lur’e systems. Chaos Solitons Fractals 39, 1440–1446 (2009) · Zbl 1197.93149 [18] Li, C.D., Liao, X.F., Zhang, R.: A unified approach for impulsive lag synchronization of chaotic systems with time delay. Chaos Solitons Fractals 23, 1177–1184 (2005) · Zbl 1080.37033 [19] Wang, D.X., Zhong, Y.L., Chen, S.H.: Lag synchronizing chaotic system based on a single controller. Commun. Nonlinear Sci. Numer. Simul. 13, 637–644 (2008) · Zbl 1130.34322 [20] Lu, J.F.: Generalized (complete, lag, anticipated) synchronization of discrete-time chaotic systems. Commun. Nonlinear Sci. Numer. Simul. 13, 1851–1859 (2008) · Zbl 1221.37216 [21] Zheng, Y.A., Nian, Y.B., Liu, Z.R.: Impulsive control for the stabilization of discrete chaotic system. Chin. Phys. Lett. 19, 1251–1253 (2002) [22] Zheng, Y.A., Nian, Y.B., Liu, Z.R.: Impulsive synchronization of discrete chaotic systems. Chin. Phys. Lett. 20, 199–201 (2003) 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.