Robust exponential stability of impulsive stochastic neural networks with leakage time-varying delay. (English) Zbl 1474.93232
Summary: This paper investigates mean-square robust exponential stability of the equilibrium point of stochastic neural networks with leakage time-varying delays and impulsive perturbations. By using Lyapunov functions and Razumikhin techniques, some easy-to-test criteria of the stability are derived. Two examples are provided to illustrate the efficiency of the results.
MSC:
| 93E15 | Stochastic stability in control theory |
| 34K45 | Functional-differential equations with impulses |
| 34K50 | Stochastic functional-differential equations |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
References:
| [1] | Zhao, H., Global exponential stability and periodicity of cellular neural networks with variable delays, Physics Letters A, 336, 4-5, 331-341 (2005) · Zbl 1136.34348 · doi:10.1016/j.physleta.2004.12.001 |
| [2] | Wang, Y.; Lu, C.; Ji, G.; Wang, L., Global exponential stability of high-order Hopfield-type neural networks with S-type distributed time delays, Communications in Nonlinear Science and Numerical Simulation, 16, 8, 3319-3325 (2011) · Zbl 1221.34204 · doi:10.1016/j.cnsns.2010.11.005 |
| [3] | Wang, L.; Zhang, R.; Wang, Y., Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays, Nonlinear Analysis: Real World Applications, 10, 2, 1101-1113 (2009) · Zbl 1167.35404 · doi:10.1016/j.nonrwa.2007.12.002 |
| [4] | Gopalsamy, K., Leakage delays in BAM, Journal of Mathematical Analysis and Applications, 325, 2, 1117-1132 (2007) · Zbl 1116.34058 · doi:10.1016/j.jmaa.2006.02.039 |
| [5] | Li, X.; Fu, X.; Balasubramaniam, P., 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 |
| [6] | Li, X.; Rakkiyappan, R.; Balasubramaniam, P., Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations, Journal of the Franklin Institute, 348, 2, 135-155 (2011) · Zbl 1241.92006 · doi:10.1016/j.jfranklin.2010.10.009 |
| [7] | Wang, Y.; Zheng, C.; Feng, E., Stability analysis of mixed recurrent neural networks with time delay in the leakage term under impulsive perturbations, Neurocomputing, 119, 454-461 (2013) · doi:10.1016/j.neucom.2013.03.012 |
| [8] | Long, S.; Song, Q.; Wang, X.; Li, D., Stability analysis of fuzzy cellular neural networks with time delay in the leakage term and impulsive perturbations, Journal of the Franklin Institute, 349, 7, 2461-2479 (2012) · Zbl 1287.93049 · doi:10.1016/j.jfranklin.2012.05.009 |
| [9] | Li, X.; Fu, X., Effect of leakage time-varying delay on stability of nonlinear differential systems, Journal of the Franklin Institute, 350, 6, 1335-1344 (2013) · Zbl 1293.34065 · doi:10.1016/j.jfranklin.2012.04.007 |
| [10] | Liu, B., Global exponential stability for BAM neural networks with time-varying delays in the leakage terms, Nonlinear Analysis: Real World Applications, 14, 1, 559-566 (2013) · Zbl 1260.34138 · doi:10.1016/j.nonrwa.2012.07.016 |
| [11] | Park, M.; Kwon, O.; Park, J.; Lee, S.; Cha, E., Synchronization criteria for coupled stochastic neural networks with time-varying delays and leakage delay, Journal of the Franklin Institute, 349, 5, 1699-1720 (2012) · Zbl 1254.93012 · doi:10.1016/j.jfranklin.2012.02.002 |
| [12] | Gan, Q.; Liang, Y., Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control, Journal of the Franklin Institute, 349, 6, 1955-1971 (2012) · Zbl 1300.93113 · doi:10.1016/j.jfranklin.2012.05.001 |
| [13] | Guan, Z.; Lam, J.; Chen, G., On impulsive autoassociative neural networks, Neural Networks, 13, 1, 63-69 (2000) · doi:10.1016/S0893-6080(99)00095-7 |
| [14] | Guan, Z.; Chen, G., On delayed impulsive Hopfield neural networks, Neural Networks, 12, 2, 273-280 (1999) · doi:10.1016/S0893-6080(98)00133-6 |
| [15] | Haykin, S., Neural Networks (1994), Upper Saddle River, NJ, USA: Prentice-Hall, Upper Saddle River, NJ, USA · Zbl 0828.68103 |
| [16] | Liang, X.; Wang, L., Exponential stability for a class of stochastic reaction-diffusion Hopfield neural networks with delays, Journal of Applied Mathematics, 2012 (2012) · Zbl 1244.93121 · doi:10.1155/2012/693163 |
| [17] | Li, D.; Wang, X.; Xu, D., Existence and global \(p\)-exponential stability of periodic solution for impulsive stochastic neural networks with delays, Nonlinear Analysis. Hybrid Systems, 6, 3, 847-858 (2012) · Zbl 1244.93169 · doi:10.1016/j.nahs.2011.11.002 |
| [18] | Chen, W.; Zheng, W. X., Robust stability and \(H_\infty \)-control of uncertain impulsive systems with time-delay, Automatica, 45, 1, 109-117 (2009) · Zbl 1154.93406 · doi:10.1016/j.automatica.2008.05.020 |
| [19] | Cheng, P.; Deng, F.; Peng, Y., Robust exponential stability and delayed-state-feedback stabilization of uncertain impulsive stochastic systems with time-varying delay, Communications in Nonlinear Science and Numerical Simulation, 17, 12, 4740-4752 (2012) · Zbl 1263.93232 · doi:10.1016/j.cnsns.2012.03.038 |
| [20] | Zhang, Y., Robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses, Neurocomputing, 74, 17, 3268-3276 (2011) · doi:10.1016/j.neucom.2011.05.004 |
| [21] | Wu, S.; Li, K.; Huang, T., Global exponential stability of static neural networks with delay and impulses: discrete-time case, Communications in Nonlinear Science and Numerical Simulation, 17, 10, 3947-3960 (2012) · Zbl 1253.92003 · doi:10.1016/j.cnsns.2012.02.013 |
| [22] | Wang, Y.; Xie, L.; de Souza, C. E., Robust control of a class of uncertain nonlinear systems, Systems and Control Letters, 19, 2, 139-149 (1992) · Zbl 0765.93015 · doi:10.1016/0167-6911(92)90097-C |
| [23] | Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), Philadelphia, Pa, USA: Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA · Zbl 0816.93004 · doi:10.1137/1.9781611970777 |
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.
