Robust synchronization criterion for coupled stochastic discrete-time neural networks with interval time-varying delays, leakage delay, and parameter uncertainties. (English) Zbl 1274.93251

Summary: The purpose of this paper is to investigate a delay-dependent robust synchronization analysis for coupled stochastic discrete-time neural networks with interval time-varying delays in networks coupling, a time delay in leakage term, and parameter uncertainties. Based on the Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii’s functional and utilizing Finsler’s lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.


93E03 Stochastic systems in control theory (general)
93E15 Stochastic stability in control theory
93C55 Discrete-time control/observation systems
Full Text: DOI


[1] Strogatz, S. H., Exploring complex networks, Nature, 410, 6825, 268-276 (2001) · Zbl 1370.90052 · doi:10.1038/35065725
[2] Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D.-U., Complex networks: structure and dynamics, Physics Reports A, 424, 4-5, 175-308 (2006) · Zbl 1371.82002 · doi:10.1016/j.physrep.2005.10.009
[3] Cao, J.; Chen, G.; Li, P., Global synchronization in an array of delayed neural networks with hybrid coupling, IEEE Transactions on Systems, Man, and Cybernetics, Part B, 38, 2, 488-498 (2008) · doi:10.1109/TSMCB.2007.914705
[4] Cao, J.; Li, L., Cluster synchronization in an array of hybrid coupled neural networks with delay, Neural Networks, 22, 4, 335-342 (2009) · Zbl 1338.93284 · doi:10.1016/j.neunet.2009.03.006
[5] Li, T.; Wang, T.; Song, A. G.; Fei, S. M., Exponential synchronization for arrays of coupled neural networks with time-delay couplings, International Journal of Control, Automation and Systems, 9, 1, 187-196 (2011) · doi:10.1007/s12555-011-0124-4
[6] Kwon, O. M.; Park, J. H.; Lee, S. M., Secure communication based on chaotic synchronization via interval time-varying delay feedback control, Nonlinear Dynamics, 63, 1-2, 239-252 (2011) · Zbl 1215.93127 · doi:10.1007/s11071-010-9800-9
[7] Liu, Y.; Wang, Z.; Liang, J.; Liu, X., Synchronization and state estimation for discrete-time complex networks with distributed delays, IEEE Transactions on Systems, Man, and Cybernetics, Part B, 38, 5, 1314-1325 (2008) · doi:10.1109/TSMCB.2008.925745
[8] Yue, D.; Li, H., Synchronization stability of continuous/discrete complex dynamical networks with interval time-varying delays, Neurocomputing, 73, 4-6, 809-819 (2010) · doi:10.1016/j.neucom.2009.10.008
[9] Li, T.; Song, A.; Fei, S., Synchronization control for arrays of coupled discrete-time delayed Cohen-Grossberg neural networks, Neurocomputing, 74, 1-3, 197-204 (2010) · doi:10.1016/j.neucom.2010.02.018
[10] Xu, S.; Lam, J.; Mao, X.; Zou, Y., A new LMI condition for delay-dependent robust stability of stochastic time-delay systems, Asian Journal of Control, 7, 4, 419-423 (2005) · doi:10.1111/j.1934-6093.2005.tb00404.x
[11] Wu, Z.; Su, H.; Chu, J.; Zhou, W., Improved result on stability analysis of discrete stochastic neural networks with time delay, Physics Letters A, 373, 17, 1546-1552 (2009) · Zbl 1228.92004 · doi:10.1016/j.physleta.2009.02.056
[12] Yang, R.; Shi, P.; Gao, H., New delay-dependent stability criterion for stochastic systems with time delays, IET Control Theory & Applications, 2, 11, 966-973 (2008) · doi:10.1049/iet-cta:20070437
[13] Kwon, O. M., Stability criteria for uncertain stochastic dynamic systems with time-varying delays, International Journal of Robust and Nonlinear Control, 21, 3, 338-350 (2011) · Zbl 1213.93201 · doi:10.1002/rnc.1600
[14] Li, H.; Yue, D., Synchronization of Markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time-varying delays, Journal of Physics A, 43, 10 (2010) · Zbl 1198.60040 · doi:10.1088/1751-8113/43/10/105101
[15] Wang, H.; Song, Q., Synchronization for an array of coupled stochastic discrete-time neural networks with mixed delays, Neurocomputing, 74, 10, 1572-1584 (2011) · doi:10.1016/j.neucom.2011.01.014
[16] Tang, Y.; Fang, J. A., Robust synchronization in an array of fuzzy delayed cellular neural networks with stochastically hybrid coupling, Neurocomputing, 72, 13-15, 3253-3262 (2009) · doi:10.1016/j.neucom.2009.02.010
[17] Liang, J.; Wang, Z.; Liu, Y.; Liu, X., Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks, IEEE Transactions on Neural Networks, 19, 11, 1910-1921 (2008) · doi:10.1109/TNN.2008.2003250
[18] Song, Q., Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling, Applied Mathematics and Computation, 216, 5, 1605-1613 (2010) · Zbl 1194.34145 · doi:10.1016/j.amc.2010.03.014
[19] Song, Q., Design of controller on synchronization of chaotic neural networks with mixed time-varying delays, Neurocomputing, 72, 13-15, 3288-3295 (2009) · doi:10.1016/j.neucom.2009.02.011
[20] Song, Q., Synchronization analysis of coupled connected neural networks with mixed time delays, Neurocomputing, 72, 16-18, 3907-3914 (2009) · doi:10.1016/j.neucom.2009.04.009
[21] Huang, T.; Li, C.; Duan, S.; Starzyk, J., Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects, IEEE Transactions on Neural Networks and Learning Systems, 23, 866-875 (2012)
[22] Li, X.; Fu, X.; Balasubramaniam, P.; Rakkiyappan, R., Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations, Nonlinear Analysis: Real World Applications, 11, 5, 4092-4108 (2010) · Zbl 1205.34108 · doi:10.1016/j.nonrwa.2010.03.014
[23] Li, X.; Cao, J., Delay-dependent stability of neural networks of neutral type with time delay in the leakage term, Nonlinearity, 23, 7, 1709-1726 (2010) · Zbl 1196.82102 · doi:10.1088/0951-7715/23/7/010
[24] Xu, S.; Lam, J., A survey of linear matrix inequality techniques in stability analysis of delay systems, International Journal of Systems Science, 39, 12, 1095-1113 (2008) · Zbl 1156.93382 · doi:10.1080/00207720802300370
[25] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory. Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, 15, xii+193 (1994), Philadelphia, Pa, USA: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA · Zbl 0816.93004 · doi:10.1137/1.9781611970777
[26] Kwon, O. M.; Lee, S. M.; Park, J. H., On improved passivity criteria of uncertain neural networks with time-varying delays, Nonlinear Dynamics, 67, 1261-1271 (2011) · Zbl 1243.93028 · doi:10.1007/s11071-011-0067-6
[27] Godsil, C.; Royle, G., Algebraic Graph Theory. Algebraic Graph Theory, Graduate Texts in Mathematics, 207, xx+439 (2001), New York, NY, USA: Springer, New York, NY, USA · Zbl 0968.05002 · doi:10.1007/978-1-4613-0163-9
[28] Park, M. J.; Kwon, O. M.; Park, J. H.; Lee, S. M.; Cha, E. J., Leader following consensus criteria for multi-agent systems with time-varying delays and switching interconnection topologies, Chinese Physics B, 21 (2012) · doi:10.1088/1674-1056/21/11/110508
[29] Graham, A., Kronecker Products and Matrix Calculus: With Applications (1982), New York, NY, USA: John Wiley & Sons, New York, NY, USA
[30] Zhu, X. L.; Yang, G. H., Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay, Proceedings of the American Control Conference (ACC ’08) · doi:10.1109/ACC.2008.4586727
[31] de Oliveira, M. C.; Skelton, R. E., Stability tests for constrained linear systems, Perspectives in Robust Control. Perspectives in Robust Control, Lecture Notes in Control and Information Sciences, 268, 241-257 (2001), London, UK: Springer, London, UK · Zbl 0997.93086 · doi:10.1007/BFb0110624
[32] Park, P.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 1, 235-238 (2011) · Zbl 1209.93076 · doi:10.1016/j.automatica.2010.10.014
[33] Barabási, A.-L.; Albert, R., Emergence of scaling in random networks, American Association for the Advancement of Science, 286, 5439, 509-512 (1999) · Zbl 1226.05223 · doi:10.1126/science.286.5439.509
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.