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2011 | 21 | 1 | 127-135
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
21
Numer
1
Strony
127-135
Opis fizyczny
Daty
wydano
2011
otrzymano
2010-03-08
poprawiono
2010-09-07
Twórcy
  • Department of Mathematics, Periyar University, Salem 636 011, India
  • Department of Mathematics, Sungkyunkwan University, Suwon 440-746, South Korea
  • Department of Mathematics, Anna University of Technology, Coimbatore 641 047, India
autor
  • Department of Mathematics, Sungkyunkwan University, Suwon 440-746, South Korea
Bibliografia
  • 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.
  • 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.
  • Cichocki, A. and Unbehauen, R. (1993). Neural Networks for Optimization and Signal Processing, Wiley, Chichester.
  • 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.
  • Gu, K., Kharitonov, V. and Chen, J. (2003). Stability of TimeDelay Systems, Birkhäuser, Boston, MA.
  • Haykin, S. (1998). Neural Networks: A Comprehensive Foundation, Prentice Hall, Upper Saddle River, NJ.
  • 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.
  • 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.
  • 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.
  • 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.
  • Mao, X. (2002). Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Transactions on Automatic Control 47(10): 1604-1612.
  • 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.
  • 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.
  • Singh, V. (2007). On global robust stability of interval Hopfield neural networks with delay, Chaos, Solitons & Fractals 33(4): 1183-1188.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Zhang, Y. and Sun, J.T. (2005). Stability of impulsive neural networks with time delays, Physics Letters A 348(1-2): 44-50.
  • Zhou, Q. and Wan, L. (2008). Exponential stability of stochastic delayed Hopfield neural networks, Applied Mathematics and Computation 199(1): 84-89.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv21i1p127bwm
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