# zbMATH — the first resource for mathematics

Improved delay-partitioning method to stability analysis for neural networks with discrete and distributed time-varying delays. (English) Zbl 1334.92025
Summary: In this paper, an improved method is derived for the delay-dependent stability problem of neural networks with discrete and distributed time-varying delays. An improved Lyapunov functional is constructed by introducing the newly delay-partitioning method and considering the sufficient information of neuron activation functions. By using the relationship between each subinterval and time-varying delay sufficiently, a new delay-dependent stability criterion has been obtained to reduce the conservatism. Two numerical examples are finally given to show the merits of the derived conditions.

##### MSC:
 92B20 Neural networks for/in biological studies, artificial life and related topics
Full Text:
##### References:
 [1] Arik, S., Global asymptotic stability of a larger class of neural networks with constant time delay, Phys. Lett. A, 311, 504-511, (2002) · Zbl 1098.92501 [2] Cao, J.; Wang, J., Global asymptotic and robust stability of recurrent neural networks with time delays, IEEE Trans. Circuits Syst. I, 52, 417-426, (2005) · Zbl 1374.93285 [3] Ji, D. H.; Koo, J. H.; Won, S. C.; Lee, S. M.; Park, J. H., Passivity-based control for Hopfield neural networks using convex representation, Appl. Math. Comput., 217, 6168-6175, (2011) · Zbl 1209.93056 [4] Hua, C.; Long, C.; Guan, X., New results on stability analysis of neural networks with time-varying delays, Phys. Lett. A, 352, 335-340, (2006) · Zbl 1187.34099 [5] He, Y.; Wu, M.; She, J. H., Delay-dependent exponential stability of delayed neural networks with time-varying delay, IEEE Trans. Circuits Syst. II, 53, 553-557, (2006) [6] He, Y.; Liu, G.; Rees, D., New delay-dependent stability criteria for neural networks with time-varying delay, IEEE Trans. Neural Networks, 18, 310-314, (2007) [7] He, Y.; Liu, G.; Rees, D.; Wu, M., Stability analysis for neural networks with time-varying interval delay, IEEE Trans. Neural Networks, 18, 1850-1854, (2007) [8] Li, T.; Ye, X. L., Improved stability criteria of neural networks with time-varying delays: an augmented LKF approach, Neurocomputing, 73, 1038-1047, (2010) [9] Kwon, O. M.; Lee, S. M.; Park, J. H.; Cha, E. J., New approaches on stability criteria for neural networks with interval time-varying delays, Appl. Math. Comput., 218, 9953-9964, (2012) · Zbl 1253.34066 [10] Li, T.; Zheng, W.; Lin, C., Delay-slope-dependent stability results of recurrent neural networks, IEEE Trans. Neural Networks, 22, 2138-2143, (2011) [11] Chen, W. H.; Lu, X.; Guan, Z. H.; Zheng, W. X., Delay-dependent exponential stability of neural networks with variable delay: an LMI approach, IEEE Trans. Circuits Syst. II, 53, 837-842, (2006) [12] Kwon, O. M.; Park, J. H., Improved delay-dependent stability criterion for neural networks with time-varying delays, Phys. Lett. A, 373, 529-535, (2009) · Zbl 1227.34030 [13] Xiao, S.; Zhang, X., New globally asymptotic stability criteria for delayed cellular neural networks, IEEE Trans. Circuits Syst. II, 56, 659-663, (2009) [14] Tian, J.; Xie, X., New asymptotic stability criteria for neural networks with time-varying delay, Phys. Lett. A, 374, 938-943, (2010) · Zbl 1235.92007 [15] Mou, S.; Gao, H.; Lam, J., A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay, IEEE Trans. Neural Networks, 19, 532-535, (2008) [16] Zhang, H.; Liu, Z.; Huang, G.; Wang, Z., Novel weighting-delaybased stability criteria for recurrent neural networks with time-varying delay, IEEE Trans. Neural Networks, 21, 91-106, (2010) [17] Zhang, X.; Han, Q., New Lyapunov-krasovskii functionals for global asymptotic stability of delayed neural networks, IEEE Trans. Neural Networks, 20, 533-539, (2009) [18] Hu, L.; Gao, H.; Shi, P., New stability criteria for Cohen-Grossberg neural networks with time delays, IET Control Theory Appl., 3, 1275-1282, (2009) [19] Zeng, H.; He, Y.; Wu, M.; Zhang, C., Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays, IEEE Trans. Neural Networks, 22, 806-812, (2011) [20] Ge, C.; Hua, C.; Guan, X., New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach, (2013), IEEE Trans. Neural Networks Article in perss [21] Zhu, X.; Wang, Y., Delay-dependent exponential stability for neural networks with discrete and distributed time-varying delays, Phys. Lett. A, 373, 4066-4072, (2009) · Zbl 1234.92004 [22] Yue, D.; Zhang, Y.; Tian, E.; Peng, C., Delay-distribution-dependent exponential stability criteria for discrete-time recurrent neural networks with stochastic delay, IEEE Trans. Neural Networks, 19, 1299-1306, (2008) [23] Sun, J.; Liu, G.; Chen, J.; Rees, D., Improved stability criteria for neural networks with time-varying delay, Phys. Lett. A, 373, 342-348, (2009) · Zbl 1227.92003 [24] Park, J. H.; Kwon, O. M., Further results on state estimation for neural networks of neutral-type with time-varying delay, Appl. Math. Comput., 208, 69-75, (2009) · Zbl 1169.34334 [25] Liu, Y.; Wang, Z.; Liu, X., Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural Networks, 19, 667-675, (2006) · Zbl 1102.68569 [26] Xu, S.; Lam, J., A new approach to exponential stability analysis of neural networks with time-varying delays, Neural Networks, 19, 76-83, (2006) · Zbl 1093.68093 [27] Kwon, O. M.; Park, J. H.; Lee, S. M.; Cha, E. J., A new augmented Lyapunov-krasovskii functional approach to exponential passivity for neural networks with time-varying delays, Appl. Math. Comput., 217, 10231-10238, (2011) · Zbl 1225.93096 [28] Song, Q.; Wang, Z., A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays, Phys. Lett. A, 368, 134-145, (2007) [29] Liao, X.; Chen, G.; Sanchez, E. N., Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach, Neural Networks, 15, 855-866, (2002) [30] Mou, S.; Gao, H.; Qiang, W.; Chen, K., New delay-dependent exponential stability for neural networks with time delay, IEEE Trans. Syst. Man Cybern. Part B: Cybern., 38, 571-576, (2009) [31] Wang, Z.; Liu, Y.; Li, M.; Liu, X., Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Trans. Neural Networks, 17, 814-820, (2006) [32] Li, H.; Chen, B.; Zhou, Q.; Qian, W., Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters, IEEE Trans. Syst. Man Cybern. Part B: Cybern., 39, 94-102, (2009) [33] Zhao, H.; Cao, J., New conditions for global exponential stability of cellular neural networks with delays, Neural Networks, 18, 1332-1340, (2005) · Zbl 1083.68108 [34] Lakshmanan, S.; Park, J. H.; Jung, H. Y.; Balasubramaniam, P., Design of state estimator for neural networks with leakage, discrete and distributed delays, Appl. Math. Comput., 218, 11297-11310, (2012) · Zbl 1277.93078 [35] Wu, Z. G.; Park, J. H.; He, H. Y.; Chu, J., Passivity analysis of Markov jump neural networks with mixed time-delays and piecewise-constant transition rates, Nonlinear Anal.: Real World Appl., 13, 2423-2431, (2012) · Zbl 1260.60172 [36] Mathiyalagan, K.; Sakthivel, R.; Marshal Anthoni, S., New stability and stabilization criteria for fuzzy neural networks with various activation functions, Phys. Scr., 84, 015007, (2011) · Zbl 1219.82131 [37] Sakthivel, R.; Mathiyalagan, K.; Marshal Anthoni, S., Delay-dependent robust stabilization and $$H_\infty$$ control for neural networks with various activation functions, Phys. Scr., 85, 045801, (2012) · Zbl 1243.93085 [38] Mathiyalagan, K.; Sakthivel, R.; Marshal Anthoni, S., New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays, Commun. Nonlinear Sci. Numer. Simul., 17, 1392-1407, (2012) · Zbl 1239.93112 [39] Sakthivel, R.; Arunkumar, A.; Mathiyalagan, K.; Marshal Anthoni, S., Robust passivity analysis of fuzzy Cohen-Grossberg BAM neural networks with time-varying delays, Appl. Math. Comput., 218, 3799-3809, (2011) · Zbl 1257.34059 [40] Sakthivel, R.; Mathiyalagan, K.; Marshal Anthoni, S., Robust $$H_\infty$$ control for uncertain discrete-time stochastic neural networks with time-varying delays, IET Control Theory Appl., 6, 1220-1228, (2012) · Zbl 1268.93118 [41] Wang, J.; Park, Ju H.; Shen, H.; Wang, J., Delay-dependent robust dissipativity conditions for delayed neural networks with random uncertainties, Appl. Math. Comput., 221, 710-719, (2013) · Zbl 1329.93150 [42] Lee, Tae H.; Park, Ju H.; Kwon, O. M.; Lee, S. M., Stochastic sampled-data control for state estimation of time-varying delayed neural networks, Neural Networks, 46, 99-108, (2013) · Zbl 1296.93184 [43] Park, Ju H., On global stability criterion of neural networks with continuously distributed delays, Chaos Solitons Fract., 37, 444-449, (2008) · Zbl 1141.93054 [44] Song, Q.; Cao, J., Dynamics of bidirectional associative memory networks with distributed delays and reaction-diffusion terms, Nonlinear Anal.: Real World Appl., 8, 345-361, (2007) · Zbl 1114.35103 [45] Song, Q.; Wang, Z., New results on passivity analysis of uncertain neural networks with time-varying delays, Int. J. Comput. Math., 87, 668-678, (2010) · Zbl 1186.68392 [46] Boyd, S.; Balakrishnan, V.; Feron, E.; El Ghaoui, L., Linear matrix inequalities in systems and control, (1994), SIMA Philadelphia, Pa, USA · Zbl 0816.93004 [47] Park, P. G.; 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 [48] Hale, J., Theory of functional differential equation, (1977), Springer New York
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.