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International Journal of Applied Mathematics and Computer Science

Journal of University of Zielona Gora and Lubuskie Scientific Society

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Volume 21, Issue 1


Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays

Ramachandran Raja / Rathinasamy Sakthivel / Selvaraj Anthoni / Hyunsoo Kim
Published Online: 2011-03-28 | DOI: https://doi.org/10.2478/v10006-011-0009-y

Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays

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.

Keywords: Hopfield neural networks; Markovian jumping; stochastic stability; Lyapunov function; impulses

  • 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.Web of ScienceGoogle Scholar

  • Balasubramaniam, P. and Rakkiyappan, R. (2009). Delay-dependent robust stability analysis of uncertain stochastic neural networks with discrete interval and distributed time-varying delays, Neurocomputing 72(13-15): 3231-3237.Google Scholar

  • Cichocki, A. and Unbehauen, R. (1993). Neural Networks for Optimization and Signal Processing, Wiley, Chichester.Google Scholar

  • 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.Web of ScienceGoogle Scholar

  • Gu, K., Kharitonov, V. and Chen, J. (2003). Stability of Time-Delay Systems, Birkhäuser, Boston, MA.PubMedGoogle Scholar

  • Haykin, S. (1998). Neural Networks: A Comprehensive Foundation, Prentice Hall, Upper Saddle River, NJ.Google Scholar

  • 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.Web of ScienceGoogle Scholar

  • 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.Web of ScienceGoogle Scholar

  • 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.Google Scholar

  • 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.Web of ScienceCrossrefGoogle Scholar

  • Mao, X. (2002). Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Transactions on Automatic Control 47(10): 1604-1612.Web of ScienceGoogle Scholar

  • 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.Google Scholar

  • 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.CrossrefWeb of ScienceGoogle Scholar

  • Singh, V. (2007). On global robust stability of interval Hop-field neural networks with delay, Chaos, Solitons & Fractals 33(4): 1183-1188.CrossrefGoogle Scholar

  • 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.Web of ScienceGoogle Scholar

  • Song, Q. and Zhang, J. (2008). Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays, Nonlinear Analysis: Real World Applications 9(2): 500-510.Google Scholar

  • 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.Web of ScienceGoogle Scholar

  • 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.Web of ScienceCrossrefGoogle Scholar

  • 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.Web of ScienceCrossrefGoogle Scholar

  • Zhang, Y. and Sun, J. T. (2005). Stability of impulsive neural networks with time delays, Physics Letters A 348(1-2): 44-50.Google Scholar

  • Zhou, Q. and Wan, L. (2008). Exponential stability of stochastic delayed Hopfield neural networks, Applied Mathematics and Computation 199(1): 84-89.Web of ScienceGoogle Scholar

About the article

Published Online: 2011-03-28

Published in Print: 2011-03-01

Citation Information: International Journal of Applied Mathematics and Computer Science, Volume 21, Issue 1, Pages 127–135, ISSN (Print) 1641-876X, DOI: https://doi.org/10.2478/v10006-011-0009-y.

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