Stability conditions concerning neutral-type BAM neural networks with infinite distributed delay. (English) Zbl 1538.93032
Summary: This paper presents a class model for neutral-type bidirectional associative memory (BAM) neural networks (NNS) with infinite distributed delay. The model extends and improves some recent works for BAM-NNS. Based on the Lyapunov-Krasovskii functional (LKF) theory, the linear matrix inequality (LMI) method and some analysis techniques, the novel stability criteria for such model are obtained. Four numerical examples prove the validity and less conservativeness of the proposed criteria. The developed results are helpful to design of an actual system.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93B70 | Networked control |
| 93C43 | Delay control/observation systems |
Keywords:
global stability; neutral type; Lyapunov functional; BAM neural networks; infinite distributed delaysReferences:
| [1] | Aouiti, C.; Gharbia, I. B.; Cao, J. D.; Alsaedi, A., Dynamics of impulsive neutral-type BAM neural networks, J. Franklin. I., 81, 2294-2324 (2019) · Zbl 1409.93016 · doi:10.1016/j.jfranklin.2019.01.028 |
| [2] | Aouiti, C.; Gharbia, I. B.; Cao, J.; M’hamdi, M. S.; Alsaedi, A., Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms, Chaos. Solitons. Fract., 107, 111-127 (2018) · Zbl 1380.92006 · doi:10.1016/j.chaos.2017.12.022 |
| [3] | Balasubramaniam, P.; Rakkiyappan, R., Global exponential stability for neutral-type BAM neural networks with time-varying delays, Int. J. Comput. Math., 87, 2064-2075 (2010) · Zbl 1205.34091 · doi:10.1080/00207160802588544 |
| [4] | Balasubramaniam, P.; Vembarasan, V., Asymptotic stability of BAM neural networks of neutral-type with impulsive effects and time delay in the leakage term, Int. J. Comput. Math., 88, 3271-3291 (2011) · Zbl 1247.34122 · doi:10.1080/00207160.2011.591388 |
| [5] | Cao, J. D.; Wang, L., Periodic oscillatory solution of bidirectional associative memory networks with delays, Phys. Rev. E, 61, 1825-1828 (2000) · doi:10.1103/PhysRevE.61.1825 |
| [6] | Cao, J. D.; Ying, W., Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays, Neural Netw., 53, 165-172 (2014) · Zbl 1322.93087 · doi:10.1016/j.neunet.2014.02.003 |
| [7] | Chen, B.; Yu, L.; Zhang, W. A., Exponential convergence rate estimation for neutral BAM neural networks with mixed time-delays, Neural. Comput. Appl., 20, 451-460 (2011) · doi:10.1007/s00521-010-0415-3 |
| [8] | Elsen, I., Kraiss, K., and Krumbiegel, D., Pixel Based 3D Object Recognition with Bidirectional Associative Memories, Proceedings of International Joint Conference on Neural Networks(ICNN’97). 3(1997), pp. 1679-1684. |
| [9] | Gau, R. S.; Hsieh, J. G.; Lien, C. H., Global exponential stability for uncertain bidirectional associative memory neural networks with multiple time-varying delays via LMI approach, Int. J. Circ. Theory. App., 36, 451-471 (2008) · Zbl 1191.94141 · doi:10.1002/cta.449 |
| [10] | Huang, C. D.; Cao, J. D., Impact of leakage delay on bifurcation in high-order fractional BAM neural networks, Neural Netw., 98, 223-235 (2018) · Zbl 1439.93004 · doi:10.1016/j.neunet.2017.11.020 |
| [11] | Huang, C. D.; Meng, Y. J.; Cao, J. D.; Ahmed, A.; Alsaadi, F. E., New bifurcation results for fractional BAM neural network with leakage delay, Chaos. Solitons. Fract., 100, 31-44 (2017) · Zbl 1373.34117 · doi:10.1016/j.chaos.2017.04.037 |
| [12] | Kosko, B., Adaptive bidirectional associative memories, Appl. Opt., 26, 4947-4960 (1987) · doi:10.1364/AO.26.004947 |
| [13] | Kosko, B., Bidirectional associative memories, IEEE T. Syst. Man. Cy-s, 18, 49-60 (1988) · doi:10.1109/21.87054 |
| [14] | Li, H.; Li, C.; Huang, T.; Zhang, W., Fixed-time stabilization of impulsive Cohen-grossberg BAM neural networks, Neural Netw., 98, 203-211 (2018) · Zbl 1441.93204 · doi:10.1016/j.neunet.2017.11.017 |
| [15] | Liu, B., Global exponential stability for BAM neural networks with time-varying delays in the leakage terms, Nonlinear, Anal.Real., 14, 559-566 (2013) · Zbl 1260.34138 · doi:10.1016/j.nonrwa.2012.07.016 |
| [16] | Liu, G. Q.; Yang, S. X., Stability criterion for BAM neural networks of neutral-type with Interval time-varying delays, Procedia. Eng., 15, 2836-2840 (2011) · doi:10.1016/j.proeng.2011.08.534 |
| [17] | Liu, J.; Zong, G., New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type, Neurocomputing, 72, 2549-2555 (2009) · doi:10.1016/j.neucom.2008.11.006 |
| [18] | Maharajan, C.; Raja, R.; Cao, J. D.; Rajchakit, G.; Alsaedi, A., Impulsive Cohen-grossberg BAM neural networks with mixed time-delays: an exponential stability analysis issue, Neurocomputing, 275, 2588-2602 (2018) · doi:10.1016/j.neucom.2017.11.028 |
| [19] | Nagamani, G.; Rajan, G. S.; Zhu, Q., Exponential state estimation for Memristor-based discrete-time BAM neural networks With Additive delay Components, IEEE. T. Cybernet., 1-12 (2019) |
| [20] | Park, J. H.; Park, C. H.; Kwon, O. M.; Lee, S. M., A new stability criterion for bidirectional associative memory neural networks of neutral-type, Appl. Math. Comput., 199, 716-722 (2008) · Zbl 1149.34345 |
| [21] | Qi, J.; Li, C.; Huang, T., Stability of inertial BAM neural network with time-varying delay via impulsive control, Neurocomputing, 161, 162-167 (2015) · doi:10.1016/j.neucom.2015.02.052 |
| [22] | Sader, M.; Abdurahman, A.; Jiang, H., General decay synchronization of delayed BAM neural networks via nonlinear feedback control, Appl. Math. Comput., 337, 302-314 (2018) · Zbl 1427.93025 |
| [23] | Sowmiya, C.; Raja, R.; Cao, J. D.; Rajchakit, G., Impulsive discrete-time BAM neural networks with random parameter uncertainties and time-varying leakage delays: an asymptotic stability analysis, Nonlinear Dynam., 91, 2571-2592 (2018) · Zbl 1392.92009 · doi:10.1007/s11071-017-4032-x |
| [24] | Wang, Y. L.; Cao, J. D., Exponential stability of stochastic higher-order BAM neural networks with reaction-diffusion terms and mixed time-varying delays, Neurocomputing, 119, 192-200 (2013) · doi:10.1016/j.neucom.2013.03.040 |
| [25] | Wang, Z.; Huang, L., Global stability analysis for delayed complex-valued BAM neural networks, Neurocomputing, 173, 2083-2089 (2016) · doi:10.1016/j.neucom.2015.09.086 |
| [26] | Zhang, H. G.; Liu, Z. W.; Huang, G. B.; Wang, Z. S., Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay, IEEE T. Neural. Networ., 21, 91-106 (2009) · doi:10.1109/TNN.2009.2034742 |
| [27] | Zhang, Z.; Liu, K.; Yang, Y., New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type, Neurocomputing, 81, 24-32 (2012) · doi:10.1016/j.neucom.2011.10.006 |
| [28] | Zhang, H. G.; Ma, T. D.; Huang, G. B.; Wang, Z. L., Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control, IEEE T. Syst. Man. Cy-s, 40, 831-844 (2009) · doi:10.1109/TSMCB.2009.2030506 |
| [29] | Zhao, Z.; Jian, J., Attracting and quasi-invariant sets for BAM neural networks of neutral-type with time-varying and infinite distributed delays, Neurocomputing, 140, 265-272 (2014) · doi:10.1016/j.neucom.2014.03.015 |
| [30] | Zhang, H. G.; Yang, F. S.; Liu, X. D.; Zhang, Q. L., Stability analysis for neural networks with time-varying delay based on quadratic convex combination, IEEE T. Neur. Net. Lear, 24, 513-521 (2013) · doi:10.1109/TNNLS.2012.2236571 |
| [31] | Zhou, H.; Zhou, Z. F.; Jiang, W., Almost periodic solutions for neutral type BAM neural networks with distributed leakage delays on time scales, Neurocomputing, 157, 223-230 (2015) · doi:10.1016/j.neucom.2015.01.013 |
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.
