×

Delay-dependent stability analysis for recurrent neural networks with time-varying delays. (English) Zbl 1264.34143

Summary: This paper concerns the problem of delay-dependent stability criteria for recurrent neural networks with time varying delays. By taking more information of states and activation functions as augmented vectors, a new class of the Lyapunov functional is proposed. Then, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

MSC:

34K20 Stability theory of functional-differential equations
93D30 Lyapunov and storage functions
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] S. Arik, “Global asymptotic stability of a larger class of neural networks with constant time delay,” Physics Letters A, vol. 311, no. 6, pp. 504-511, 2003. · Zbl 1098.92501 · doi:10.1016/S0375-9601(03)00569-3
[2] J. D. Cao, “Global asymptotic stability of neural networks with transmission delays,” International Journal of Systems Science, vol. 31, no. 10, pp. 1313-1316, 2000. · Zbl 1080.93517 · doi:10.1080/00207720050165807
[3] C. Hua, C. Long, and X. Guan, “New results on stability analysis of neural networks with time-varying delays,” Physics Letters A, vol. 352, no. 4-5, pp. 335-340, 2006. · Zbl 1187.34099 · doi:10.1016/j.physleta.2005.12.005
[4] Y. He, M. Wu, and J. H. She, “Delay-dependent exponential stability of delayed neural networks with time-varying delay,” IEEE Transactions on Circuits and Systems II, vol. 53, no. 7, pp. 553-557, 2006. · doi:10.1109/TCSII.2006.876385
[5] Y. He, G. Liu, and D. Rees, “New delay-dependent stability criteria for neural networks with yime-varying delay,” IEEE Transactions on Neural Networks, vol. 18, no. 1, pp. 310-314, 2007. · doi:10.1109/TNN.2006.888373
[6] Y. He, G. P. Liu, D. Rees, and M. Wu, “Stability analysis for neural networks with time-varying interval delay,” IEEE Transactions on Neural Networks, vol. 18, no. 6, pp. 1850-1854, 2007. · doi:10.1109/TNN.2007.903147
[7] C. Song, H. Gao, and W. Xing Zheng, “A new approach to stability analysis of discrete-time recurrent neural networks with time-varying delay,” Neurocomputing, vol. 72, no. 10-12, pp. 2563-2568, 2009. · Zbl 05719062 · doi:10.1016/j.neucom.2008.11.009
[8] J. Tian and S. Zhong, “New delay-dependent exponential stability criteria for neural networks with discrete and distributed time-varying delays,” Neurocomputing, vol. 77, no. 1, pp. 114-119, 2011. · Zbl 06017744 · doi:10.1016/j.neucom.2011.05.024
[9] T. Li and X. L. Ye, “Improved stability criteria of neural networks with time-varying delays: an augmented LKF approach,” Neurocomputing, vol. 73, no. 4-6, pp. 1038-1047, 2010. · Zbl 05721304 · doi:10.1016/j.neucom.2009.10.001
[10] W. H. Chen, X. Lu, Z. H. Guan, and W. X. Zheng, “Delay-dependent exponential stability of neural networks with variable delay: an LMI approach,” IEEE Transactions on Circuits and Systems II, vol. 53, no. 9, pp. 837-842, 2006. · doi:10.1109/TCSII.2006.881824
[11] T. Li, L. Guo, C. Sun, and C. Lin, “Further results on delay-dependent stability criteria of neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 19, no. 4, pp. 726-730, 2008. · doi:10.1109/TNN.2007.914162
[12] S. Mou, H. Gao, J. Lam, and W. Qiang, “A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay,” IEEE Transactions on Neural Networks, vol. 19, no. 3, pp. 532-535, 2008. · doi:10.1109/TNN.2007.912593
[13] L. Hu, H. Gao, and P. Shi, “New stability criteria for Cohen-Grossberg neural networks with time delays,” IET Control Theory & Applications, vol. 3, no. 9, pp. 1275-1282, 2009. · doi:10.1049/iet-cta.2008.0213
[14] R. Yang, H. Gao, and P. Shi, “Novel robust stability criteria for stochastic Hopfield neural networks with time delays,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 39, no. 2, pp. 467-474, 2009. · doi:10.1109/TSMCB.2008.2006860
[15] H. Zhang, Z. Liu, G. B. Huang, and Z. Wang, “Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay,” IEEE Transactions on Neural Networks, vol. 21, no. 1, pp. 91-106, 2010. · doi:10.1109/TNN.2009.2034742
[16] S. P. Xiao and X. M. Zhang, “New globally asymptotic stability criteria for delayed cellular neural networks,” IEEE Transactions on Circuits and Systems II, vol. 56, no. 8, pp. 659-663, 2009. · doi:10.1109/TCSII.2009.2024244
[17] X. M. Zhang and Q. L. Han, “New Lyapunov-Krasovskii functionals for global asymptotic stability of delayed neural networks,” IEEE Transactions on Neural Networks, vol. 20, no. 3, pp. 533-539, 2009. · doi:10.1109/TNN.2009.2014160
[18] H. B. Zeng, Y. He, M. Wu, and C. F. Zhang, “Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 22, no. 5, pp. 806-812, 2011. · doi:10.1109/TNN.2011.2111383
[19] T. Li, W. Zheng, and C. Lin, “Delay-slope-dependent stability results of recurrent neural networks,” IEEE Transactions on Neural Networks, vol. 22, no. 12, pp. 2138-2143, 2011.
[20] D. Yue, Y. Zhang, E. Tian, and C. Peng, “Delay-distribution-dependent exponential stability criteria for discrete-time recurrent neural networks with stochastic delay,” IEEE Transactions on Neural Networks, vol. 19, no. 7, pp. 1299-1306, 2008. · doi:10.1109/TNN.2008.2000166
[21] J. H. Park and O. M. Kwon, “Further results on state estimation for neural networks of neutral-type with time-varying delay,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 69-75, 2009. · Zbl 1169.34334 · doi:10.1016/j.amc.2008.11.017
[22] X. Zhu and Y. Wang, “Delay-dependent exponential stability for neural networks with discrete and distributed time-varying delays,” Physics Letters A, vol. 373, no. 44, pp. 4066-4072, 2009. · Zbl 1234.92004 · doi:10.1016/j.physleta.2009.09.006
[23] Z. Wang, Y. Liu, M. Li, and X. Liu, “Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 17, no. 3, pp. 814-820, 2006. · doi:10.1038/sj.bjp.0706784
[24] J. Sun, G. P. Liu, J. Chen, and D. Rees, “Improved stability criteria for neural networks with time-varying delay,” Physics Letters A, vol. 373, no. 3, pp. 342-348, 2009. · Zbl 1227.92003 · doi:10.1016/j.physleta.2008.11.048
[25] J. Tian and X. Xie, “New asymptotic stability criteria for neural networks with time-varying delay,” Physics Letters A, vol. 374, no. 7, pp. 938-943, 2010. · Zbl 1235.92007 · doi:10.1016/j.physleta.2009.12.020
[26] Q. Song and Z. Wang, “A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays,” Physics Letters A, vol. 368, no. 1-2, pp. 134-145, 2007. · doi:10.1016/j.physleta.2007.03.088
[27] X. Liao, G. Chen, and E. N. Sanchez, “Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach,” Neural Networks, vol. 15, no. 7, pp. 855-866, 2002. · Zbl 02022248 · doi:10.1016/S0893-6080(02)00041-2
[28] Y. Liu, Z. Wang, and X. Liu, “Global exponential stability of generalized recurrent neural networks with discrete and distributed delays,” Neural Networks, vol. 19, no. 5, pp. 667-675, 2006. · Zbl 1102.68569 · doi:10.1016/j.neunet.2005.03.015
[29] C. D. Zheng, L. B. Lu, and Z. S. Wang, “New LMT-based delay-dependent criterion for global asymptotic stability of cellular neural networks,” Neurocomputing, vol. 72, no. 13-15, pp. 3331-3336, 2009. · Zbl 05721118 · doi:10.1016/j.neucom.2009.01.013
[30] S. Xu and J. Lam, “A new approach to exponential stability analysis of neural networks with time-varying delays,” Neural Networks, vol. 19, no. 1, pp. 76-83, 2006. · Zbl 1093.68093 · doi:10.1016/j.neunet.2005.05.005
[31] H. Zhao and J. Cao, “New conditions for global exponential stability of cellular neural networks with delays,” Neural Networks, vol. 18, no. 10, pp. 1332-1340, 2005. · Zbl 1083.68108 · doi:10.1016/j.neunet.2004.11.010
[32] O. M. Kwon, J. H. Park, S. M. Lee, and E. J. Cha, “A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays,” Applied Mathematics and Computation, vol. 217, no. 24, pp. 10231-10238, 2011. · Zbl 1225.93096 · doi:10.1016/j.amc.2011.05.021
[33] G. B. Zhang, T. Li, and S. M. Fei, “Further stability criterion on delayed recurrent neural networks based on reciprocal convex technique,” Mathematical Problems in Engineering, vol. 2012, Article ID 829037, 14 pages, 2012. · Zbl 1264.93193 · doi:10.1155/2012/829037
[34] Y. Y. Ge, T. Li, and S. M. Fei, “Master-slave synchronization of stochastic neural networks with mixed time-varying delays,” Mathematical Problems in Engineering, vol. 2012, Article ID 730941, 18 pages, 2012. · Zbl 1264.93224 · doi:10.1155/2012/730941
[35] H. Wu, N. Li, K. Wang, G. Xu, and Q. Guo, “Global robust stability of switched interval neural networks with discrete and distributed time-varying delays of neural type,” Mathematical Problems in Engineering, vol. 2012, Article ID 361871, 18 pages, 2012. · Zbl 1264.34145 · doi:10.1155/2012/361871
[36] H. Zhang, T. Li, and S. Fei, “Synchronization for an array of coupled Cohen-Grossberg neural networks with time-varying delay,” Mathematical Problems in Engineering, vol. 2011, Article ID 831695, 22 pages, 2011. · Zbl 1213.93110 · doi:10.1155/2011/831695
[37] H. Li, H. Gao, and P. Shi, “New passivity analysis for neural networks with discrete and distributed delays,” IEEE Transactions on Neural Networks, vol. 21, no. 11, pp. 1842-1847, 2010. · doi:10.1109/TNN.2010.2059039
[38] H. Li, B. Chen, Q. Zhou, and W. Qian, “Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 39, no. 1, pp. 94-102, 2009. · doi:10.1109/TSMCB.2008.2002812
[39] S. Mou, H. Gao, W. Qiang, and K. Chen, “New delay-dependent exponential stability for neural networks with time delay,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 38, no. 2, pp. 571-576, 2008. · doi:10.1109/TSMCB.2007.913124
[40] S. Mou, H. Gao, W. Qiang, and Z. Fei, “State estimation for discrete-time neural networks with time-varying delays,” Neurocomputing, vol. 72, no. 1-3, pp. 643-647, 2008. · Zbl 05718861 · doi:10.1016/j.neucom.2008.06.009
[41] S. Mou, H. Gao, Y. Zhao, and W. Qiang, “Further improvement on synchronization stability of complex networks with coupling delays,” International Journal of Computer Mathematics, vol. 85, no. 8, pp. 1255-1263, 2008. · Zbl 1183.34116 · doi:10.1080/00207160701670310
[42] P. G. Park, J. W. Ko, and C. Jeong, “Reciprocally convex approach to stability of systems with time-varying delays,” Automatica, vol. 47, no. 1, pp. 235-238, 2011. · Zbl 1209.93076 · doi:10.1016/j.automatica.2010.10.014
[43] S. Boyd, V. Balakrishnan, E. Feron, and L. El Ghaoui, Linear Matrix Inequalities in Systems and Control, SIMA, Philadelphia, Pa, USA, 1994. · Zbl 0816.93004
[44] J. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1977. · Zbl 0352.34001
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.