- Volume 48 Issue 4
By using the Lyapunov functional method, stochastic analysis, and LMI (linear matrix inequality) approach, the mean square exponential stability of an equilibrium solution of uncertain stochastic Hopfield neural networks with delayed is presented. The proposed result generalizes and improves previous work. An illustrative example is also given to demonstrate the effectiveness of the proposed result.
stochastic Hopfield neural networks;mean square exponential stability;linear matrix inequality
- M. Basin, J. Perez, and R. Martinez-Zuniga, Optimal filtering for nonlinear polynomial systems over linear observations with delay, Int. J. Innovative Comput. Inform. Control 2 (2006), no. 4, 863-874.
- S. Blythe, X. Mao, and X. X. Liao, Stability of stochastic delay neural networks, J. Franklin Inst. 338 (2001), no. 4, 481-495. https://doi.org/10.1016/S0016-0032(01)00016-3
- E. K. Boukas and N. F. Al-Muthairi, Delay-dependent stabilization of singular linear systems with delays, Int. J. Innovative Comput. Inform. Control 2 (2006), no. 2, 283-291.
- S. Boyd, L. EI Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Philadelphia, PA, 1994.
- P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox: for Use with Matlab, The Math Works, Natick, 1995.
- C. Huang, P. Chen, Y. He, L. Huang, and W. Tan, Almost sure exponential stability of delayed Hopfield neural networks, Appl. Math. Lett. 21 (2008), no. 7, 701-705. https://doi.org/10.1016/j.aml.2007.07.030
- H. Huang, D. W. C. Ho, and J. Lam, Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE Trans. Circuits Syst. II 52 (2005), no. 5, 251-255. https://doi.org/10.1109/TCSII.2005.846305
- O. M. Kwon, J. H. Park, and S. M. Lee, On delay-dependent robust stability of uncertain neutral systems with interval time-varying delays, Appl. Math. Comput. 203 (2008), no. 2, 843-853. https://doi.org/10.1016/j.amc.2008.05.094
- T. Li, A. Song, and S. Fei, Robust stability of stochastic Cohen-Grossberg neural networks with mixed time-varying delays, Neurocomputing 73 (2009), no. 1-3, 542-551. https://doi.org/10.1016/j.neucom.2009.07.007
X. Liu and T. Chen, Robust
$\mu$-stability for uncertain stochastic neural networks with unbounded time-varying delays, Phys. A. 387 (2008), no. 12, 2952-2962. https://doi.org/10.1016/j.physa.2008.01.068
- X. Mao, Exponential Stability of Stochastic Differential Equations, Marcel Dekker, New York, 1994.
- J. H. Park, Further note on global exponential stability of uncertain cellular neural networks with variable delays, Appl. Math. Comput. 188 (2007), no. 1, 850-854. https://doi.org/10.1016/j.amc.2006.10.036
- J. H. Park and O. M. Kwon, Synchronization of neural networks of neutral type with stochastic perturbation, Modern Phys. Lett. B 23 (2009), no. 14, 1743-1751. https://doi.org/10.1142/S0217984909019909
- J. H. Park, S. M. Lee, and H. Y. Jung, LMI optimization approach to synchronization of stochastic delayed discrete-time complex networks, J. Optim. Theory Appl. 143 (2009), no. 2, 357-367. https://doi.org/10.1007/s10957-009-9562-z
- J. Qiu, J. Zhang, and P. Shi, Robust stability of uncertain linear systems with time-varying delay and nonlinear perturbations, Proc. IMechE, Part I, J. Syst. Control Eng. 220 (2006), no. 5, 411-416. https://doi.org/10.1243/09596518JSCE217
- V. Singh, Novel LMI condition for global robust stability of delayed neural networks, Chaos Solitons Fractals 34 (2007), no. 2, 503-508. https://doi.org/10.1016/j.chaos.2006.03.034
- V. Singh, Global robust stability of delayed neural networks: An LMI approach, IEEE Trans. Circuits Syst. II 52 (2005), no. 1, 33-36. https://doi.org/10.1109/TCSII.2004.840118
- V. Singh, Robust stability of cellular neural networks with delay: linear matrix inequality approach, IEE Proc. Contr. Theory Appl. 151 (2004), no. 1, 125-129. https://doi.org/10.1049/ip-cta:20040091
- L. Wan and J. Sun, Mean square exponential stability of stochastic delayed Hopfield neural networks, Phys. Lett. A 343 (2005), 306-318. https://doi.org/10.1016/j.physleta.2005.06.024
- Z. Wang, S. Lauria, J. Fang, and X. Liu, Exponential stability of uncertain stochastic neural networks with mixed time-delays, Chaos Solitons Fractals 32 (2007), no. 1, 62-72. https://doi.org/10.1016/j.chaos.2005.10.061
- Z. Wang, Y. Liu, K. Fraser, and X. Liu, Stochastic stability of unicertain Hopfield neural networks with discrete and distributed delays, Phys. Lett. A 354 (2006), no. 4, 288-297. https://doi.org/10.1016/j.physleta.2006.01.061
- J. Zhang, P. Shi, and J. Qiu, Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays, Nonlinear Anal. Real World Appl. 8 (2007), no. 4, 1349-1357. https://doi.org/10.1016/j.nonrwa.2006.06.010
- Q. Zhou and L. Wan, Exponential stability of stochastic delayed Hopfield neural net-works, Appl. Math. Comput. 199 (2008), no. 1, 84-89. https://doi.org/10.1016/j.amc.2007.09.025