The paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.
@article{bwmeta1.element.bwnjournal-article-amcv21i1p127bwm,
author = {Ramachandran Raja and Rathinasamy Sakthivel and Selvaraj Marshal Anthoni and Hyunsoo Kim},
title = {Stability of impulsive hopfield neural networks with Markovian switching and time-varying delays},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {21},
year = {2011},
pages = {127-135},
zbl = {1221.93265},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv21i1p127bwm}
}
Ramachandran Raja; Rathinasamy Sakthivel; Selvaraj Marshal Anthoni; Hyunsoo Kim. Stability of impulsive hopfield neural networks with Markovian switching and time-varying delays. International Journal of Applied Mathematics and Computer Science, Tome 21 (2011) pp. 127-135. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv21i1p127bwm/
[000] Balasubramaniam, P., Lakshmanan, S. and Rakkiyappan, R. (2009). Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties, Neurocomputing 72(16-18): 3675-3682.
[001] Balasubramaniam, P. and Rakkiyappan, R. (2009). Delaydependent robust stability analysis of uncertain stochastic neural networks with discrete interval and distributed timevarying delays, Neurocomputing 72(13-15): 3231-3237.
[002] Cichocki, A. and Unbehauen, R. (1993). Neural Networks for Optimization and Signal Processing, Wiley, Chichester. | Zbl 0824.68101
[003] Dong, M., Zhang, H. and Wang, Y. (2009). Dynamic analysis of impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays, Neurocomputing 72(7-9): 1999-2004.
[004] Gu, K., Kharitonov, V. and Chen, J. (2003). Stability of TimeDelay Systems, Birkhäuser, Boston, MA.
[005] Haykin, S. (1998). Neural Networks: A Comprehensive Foundation, Prentice Hall, Upper Saddle River, NJ. | Zbl 0828.68103
[006] Li, D., Yang, D., Wang, H., Zhang, X. and Wang, S. (2009). Asymptotic stability of multidelayed cellular neural networks with impulsive effects, Physica A 388(2-3): 218-224.
[007] Li, H., Chen, B., Zhou, Q. and Liz, C. (2008). Robust exponential stability for delayed uncertain hopfield neural networks with Markovian jumping parameters, Physica A 372(30): 4996-5003. | Zbl 1221.92006
[008] Liu, H., Zhao, L., Zhang, Z. and Ou, Y. (2009). Stochastic stability of Markovian jumping Hopfield neural networks with constant and distributed delays, Neurocomputing 72(16-18): 3669-3674.
[009] Lou, X. and Cui, B. (2009). Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters, Chaos, Solitons & Fractals 39(5): 2188-2197. | Zbl 1197.34104
[010] Mao, X. (2002). Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Transactions on Automatic Control 47(10): 1604-1612.
[011] Rakkiyappan, R., Balasubramaniam, P. and Cao, J. (2010). Global exponential stability results for neutral-type impulsive neural networks, Nonlinear Analysis: Real World Applications 11(1): 122-130. | Zbl 1186.34101
[012] Shi, P., Boukas, E. and Shi, Y. (2003). On stochastic stabilization of discrete-time Markovian jump systems with delay in state, Stochastic Analysis and Applications 21(1): 935-951. | Zbl 1024.60029
[013] Singh, V. (2007). On global robust stability of interval Hopfield neural networks with delay, Chaos, Solitons & Fractals 33(4): 1183-1188. | Zbl 1151.34333
[014] Song, Q. and Zhang, J. (2008). Global exponential stability of impulsive Cohen-Grossberg neural network with timevarying delays, Nonlinear Analysis: Real World Applications 9(2): 500-510. | Zbl 1142.34046
[015] Song, Q. and Wang, Z. (2008). Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, Physica A 387(13): 3314-3326.
[016] Wang, Z., Liu, Y., Yu, L. and Liu, X. (2006). Exponential stability of delayed recurrent neural networks with Markovian jumping parameters, Physics Letters A 356(4-5): 346-352. | Zbl 1160.37439
[017] Yuan, C.G. and Lygeros, J. (2005). Stabilization of a class of stochastic differential equations with Markovian switching, Systems and Control Letters 54(9): 819-833. | Zbl 1129.93517
[018] Zhang, H. and Wang, Y. (2008). Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Transactions on Neural Networks 19(2): 366-370.
[019] Zhang, Y. and Sun, J.T. (2005). Stability of impulsive neural networks with time delays, Physics Letters A 348(1-2): 44-50. | Zbl 1195.93122
[020] Zhou, Q. and Wan, L. (2008). Exponential stability of stochastic delayed Hopfield neural networks, Applied Mathematics and Computation 199(1): 84-89. | Zbl 1144.34389