×

zbMATH — the first resource for mathematics

Mixed time-delays dependent exponential stability for uncertain stochastic high-order neural networks. (English) Zbl 1206.65025
Authors’ abstract: This paper presents a discrete and distributed time-delays dependent simultaneous approach to deterministic and uncertain stochastic high-order neural networks. New results are proposed in terms of a linear matrix inequality by exploiting a novel Lyapunov-Krasovskii functional and by making use of novel techniques for time-delay systems. Some constraints on the systems are removed, and the new results cover some recently published works. Two numerical examples are given to show the usefulness of presented approach.

MSC:
65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65L20 Stability and convergence of numerical methods for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Dembo, A.; Farotimi, O.; Kailath, T., High-order absolutely stable neural networks, IEEE trans. circ. syst., 38, 57-65, (1991) · Zbl 0712.92002
[2] Psaltis, D.; Park, C.H.; Hong, J., Higher order associative memories and their optical implementations, Neural networks, 1, 143-163, (1988)
[3] Karayiannis, N.B.; Venetsanopoulos, A.N., On the training and performance of high-order neural networks, Math. biosci., 129, 143-168, (1995) · Zbl 0830.92005
[4] Artyomov, E.; Yadid-Pecht, O., Modified high-order neural network for invariant pattern recognition, Pattern recognit. lett., 26, 843-851, (2005)
[5] He, Y.; Wang, Q.-G.; Xie, L.; Lin, C., Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE trans. autom. control, 52, 293-299, (2007) · Zbl 1366.34097
[6] Ma, S.; Zhang, C.; Wu, Z., Delay-dependent stability and \(H_\infty\) control for uncertain discrete switched singular systems with time-delay, Appl. math. comput., 206, 413-424, (2008) · Zbl 1152.93461
[7] Rakkiyappan, R.; Balasubramaniam, P., LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays, Appl. math. comput., 204, 317-324, (2008) · Zbl 1168.34356
[8] Ibrir, S., Stability and robust stabilization of discrete-time switched systems with time-delays: LMI approach, Appl. math. comput., 206, 570-578, (2008) · Zbl 1152.93493
[9] Xie, L., Output feedback \(H_\infty\) control of systems with parameter uncertainty, Int. J. control, 63, 741-750, (1996) · Zbl 0841.93014
[10] Cao, J.; Liang, J.; Lam, J., Exponential stability of high-order bidirectional associative memory neural networks with time delays, Physica D: nonlinear phenom., 199, 425-436, (2004) · Zbl 1071.93048
[11] Ren, F.; Cao, J., LMI-based criteria for stability of high-order neural networks with time-varying delay, Nonlinear anal. ser. B: real world appl., 7, 967-979, (2006) · Zbl 1121.34078
[12] Wang, Z.; Fang, J.; Liu, X., Global stability of stochastic high-order neural networks with discrete and distributed delays, Chaos, solitons & fractals, 36, 388-396, (2008) · Zbl 1141.93416
[13] Blythe, S.; Mao, X.; Liao, X., Stability of stochastic delay neural networks, J. franklin inst., 338, 481-495, (2001) · Zbl 0991.93120
[14] Huang, H.; Ho, D.W.C.; Lam, J., Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE trans. circ. syst.: part II, 52, 251-255, (2005)
[15] Wan, L.; Sun, J., Mean square exponential stability of stochastic delayed Hopfield neural networks, Phys. lett. A, 343, 306-318, (2005) · Zbl 1194.37186
[16] Ruan, S.; Filfil, R.S., Dynamics of a two-neuron system with discrete and distributed delays, Physica D, 191, 323-342, (2004) · Zbl 1049.92004
[17] Zhao, H., Global asymptotic stability of Hopfield neural network involving distributed delays, Neural networks, 17, 47-53, (2004) · Zbl 1082.68100
[18] Zhao, H., Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays, Appl. math. comput., 154, 683-695, (2004) · Zbl 1057.34099
[19] Tang, Y.; Qiu, R.; Fang, J.; Miao, Q.; Xia, M., Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays, Phys. lett. A, 372, 4425-4433, (2008) · Zbl 1221.82078
[20] Wang, Z.; Liu, Y.; Liu, X., On global asymptotic stability of neural networks with discrete and distributed delays, Phys. lett. A, 345, 299-308, (2005) · Zbl 1345.92017
[21] Wang, Z.; Shu, H.; Liu, Y.; Ho, D.W.C.; Liu, X., Robust stability analysis of generalized neural networks with discrete and distributed time delays, Chaos, solitons & fractals, 30, 886-896, (2006) · Zbl 1142.93401
[22] Wang, Z.; Lauria, S.; Fang, J.; Liu, X., Exponential stability of uncertain stochastic neural networks with mixed time-delays, Chaos, solitons & fractals, 32, 62-72, (2007) · Zbl 1152.34058
[23] Tang, Y.; Wang, Z.; Fang, J., Pinning control of fractional-order weighted complex networks, Chaos, 19, 013112, (2009) · Zbl 1311.34018
[24] Hale, J.K., Theory of functional differential equations, (1977), Springer-Verlag New York · Zbl 0425.34048
[25] Boyd, S.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia (PA) · Zbl 0816.93004
[26] K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, pp. 2805-2810.
[27] Petersen, I.R., A stabilization algorithm for a class of uncertain linear systems, Syst. control lett., 8, 351-357, (1987) · Zbl 0618.93056
[28] Friedman, A., Stochastic differential equations and their applications, (1976), Academic Press 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.