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

International Journal of Applied Mathematics and Computer Science

Volumn 21, Issue 1, 2011, Pages 127-135

  Raja, Ramachandran ^a   Sakthivel, Rathinasamy ^b   Anthoni, Selvaraj ^c   Kim, Hyunsoo ^b  

^a PERIYAR UNIVERSITY   (India)

^b Sungkyunkwan University   (South Korea)

^c ANNA UNIVERSITY   (India)

Author keywords

Hopfield neural networks; Impulses; Lyapunov function; Markovian jumping; Stochastic stability

Indexed keywords

CONTINUOUS TIME; DELAY-DEPENDENT; IMPULSES; JUMPING PARAMETERS; LYAPUNOV; LYAPUNOV FUNCTIONALS; MARKOVIAN; MARKOVIAN JUMPING PARAMETERS; MARKOVIAN SWITCHING; MATLAB LMI TOOLBOX; NUMERICAL EXAMPLE; STABILITY ANALYSIS; STOCHASTIC STABILITY; TIME-VARYING DELAY; UPPER BOUND;

DIFFERENTIAL EQUATIONS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; MARKOV PROCESSES; NEURAL NETWORKS; STABILITY CRITERIA; STOCHASTIC SYSTEMS; SWITCHING SYSTEMS; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS;

HOPFIELD NEURAL NETWORKS;

EID: 79953203595     PISSN: 1641876X     EISSN: None     Source Type: Journal    
DOI: 10.2478/v10006-011-0009-y     Document Type: Article

References (21)

1. 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.
2. 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.
3. Cichocki, A. and Unbehauen, R. (1993). Neural Networks for Optimization and Signal Processing, Wiley, Chichester.
4. 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.
5. Gu, K., Kharitonov, V. and Chen, J. (2003). Stability of Time-Delay Systems, Birkhäuser, Boston, MA.
6. Haykin, S. (1998). Neural Networks: A Comprehensive Foundation, Prentice Hall, Upper Saddle River, NJ.
7. 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.
8. 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.
9. 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.
10. 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.
11. Mao, X. (2002). Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Transactions on Automatic Control 47(10): 1604-1612. (Pubitemid 35298547)
12. 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.
13. 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. (Pubitemid 36964285)
14. Singh, V. (2007). On global robust stability of interval Hop-field neural networks with delay, Chaos, Solitons & Fractals 33(4): 1183-1188. (Pubitemid 46412996)
15. 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.
16. 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. (Pubitemid 350267341)
17. 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. (Pubitemid 43947472)
18. 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. (Pubitemid 40915147)
19. 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. (Pubitemid 351359302)
20. Zhang, Y. and Sun, J. T. (2005). Stability of impulsive neural networks with time delays, Physics Letters A 348(1-2): 44-50. (Pubitemid 41674468)
21. Zhou, Q. and Wan, L. (2008). Exponential stability of stochastic delayed Hopfield neural networks, Applied Mathematics and Computation 199(1): 84-89. (Pubitemid 351508316)