Novel Delay-Dependent Stability Criteria for Uncertain Discrete-Time Stochastic Neural Networks with Time-Varying Delays

Authors: Mengzhuo Luo, Shouming Zhong

Abstract:

This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.

Keywords: Delay-dependent stability, Neural networks, Time varying delay, Linear matrix inequality (LMI).

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081677

References:

[1] S.Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, NJ, 1998.
[2] A.Cichoki, R.Unbehauen, Neural Networks for Optimization and Signal Processing, Wiley, Chichester, 1993.
[3] O.M.Kwon, J.H.Park, Exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays, Applied Mathematics and Computation, vol. 203, pp. 8133-823, 2008.
[4] W.Xiong, L.Song, J.Cao, Adaptive robust convergence of neural networks with time-varying delays, Nonlinear Analysis, vol. 9, pp. 1283-1291,2008.
[5] Q.Song, J.Cao, Global robust stability of interval neural networks with multiple time-varying delays, Mathematics and Computers in Simulation, vol. 74, pp. 38-46, 2007.
[6] B.Zhang, S.Xu, Y.Li, Delay-dependent robust exponential stability for uncertain recurrent neural networks with time-varying delays, International Journal of Neural Systems, vol. 17, pp. 207-218, 2007.
[7] O.M.Kwon, S.M.Lee, J.H.Park, Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays, Physics Letters A, vol. 374, pp. 1232-1241, 2010.
[8] A.Stuart, A.Humphries, Dynamical Systems and Numerical Analysis, Cambridge University, 1998.
[9] S.Hu, J.Wang, Golbal robust stability of a class of discrete-time interval neural networks, IEEE Transactions Circuits Systems, vol. 53, pp. 129- 138, 2006.
[10] Y.Liu, Z.Wang, X.Liu, Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural Networks, vol. 19, pp. 667-675, 2006.
[11] Y.Liu, Z.Wang, A.Serrano, X.Liu, Discrete-time recurrent neural networks with time-varying delays: exponential stability analysis, Physics Letters A, vol. 362, pp. 480-488, 2007.
[12] Z.Liu, S.Lv, S.Zhong, M.Ye, Improved exponential stability criteria for discrete-time neural networks with time-varying delay, Neurocomputing, vol. 73, pp, 975-985, 2010.
[13] B.Zhang, S.Xu, Y.Zou, Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays, Neurocomputing, vol. 72, pp. 321-330, 2008.
[14] J.Yu, K.Zhang, S.Fei, Exponential stability criteria for discrete-time recurrent neural networks with time-varying delay, Nonlinear Analysis: Real World Applications, vol. 11, pp. 207–216, 2010.
[15] X.Zhu, Y.Wang, G.Yang, New delay-dependent stability results for discrete-time recurrent neural networks with time-varying delay, Neurocomputing, vol. 72, pp. 3376–3383, 2009.
[16] Y.Liu, Z.Wang, X.Liu, Robust stability of discrete-time stochastic neural networks with time-varying delays, Neurocomputing, vol. 71 pp. 823–833, 2008.
[17] Y.Ou, H.Liu, Y.Si, Z.Feng, Stability analysis of discrete-time stochastic neural networks with time-varying delay, Neurocomputing, vol. 72 pp. 740–748, 2010.
[18] M.Luo, S.Zhong, R.Wang, W.Kang, Robust stability nanlysis of discretetime stochastic neural networks with time-varying delays, Applied Mathematics and Computation, vol. 209 pp. 305-313, 2009.
[19] Z.Wang, D.W.C.Ho, X.Liu, Variance-constrained filtering for uncertain stochastic systems with missing measuremants, IEEE Transactions on Automatic Control, vol. 48 pp. 1254–1258, 2003.
[20] Y.Tang, J.Fang, M.Xia, D.Yu, Delay-distribution-dependent stability of stochastic discrete-time neural networks with randomly mixed timevarying delays, Neurocomputing, vol. 72 pp. 3830–3838, 2009.
[21] Z.Wu, H.Su, J.Chu, W.Zhou, Improved results on stability analysis of discrete stochastic neural networks with the delay, Physics Letters A, vol. 373 pp. 1546–1552, 2009.
[22] Q.Song, J.Liang, Z.Wang, Passivity analysis of discrete-time stochastic neural networks with time-varying delays, Neurocomputing, vol. 72, pp. 1782–1788, 2009.
[23] Y.Zhang, D.Yue, E.Tian, Robust delay-distribution-dependent stability of discrete-time stochastic neural networks with time-vaying delay, Neurocomputing, vol. 72, pp. 1265–1273, 2009.
[24] D.Yue, Y.Zhang, E.Tian, C.Peng, Delay-distribution dependent exponential stability criteria for discrete-time recurrent neural networks with stochastic delay, IEEE Transactions on Neural Networks, vol. 18 pp. 310– 314, 2008.
[25] C.Liao, C.Lu, Design of delay-dependent state estimator for discretetime recurrent neural networks with interval discrtet and infinitedistributed time-varying delays, Cognitive Neurodynamics, vol. 5, pp. 133–143, 2011.
[26] Q.Zhu, X.Yang, H.Wang, Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances, Journal of the Franklin Institute, vol. 347, pp. 1489–1510, 2010.
[27] O.M.Kwon, J.H.Park, Delay-dependent stability for uncertain cellular neural networks with discrete and distribute time-varying delays, Journal of the Franklin Institute, vol. 345, pp. 766–778, 2008.
[28] Z.Zhang, D.Zhou, Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks, Journal of the Franklin Institute, vol. 347, pp. 763–780, 2010.
[29] J.Qiu, J.Cao, Delay-dependent exponential stability for a class of neural networks with time delays and reactionCdiffusion terms, Journal of the Franklin Institute, vol. 346, pp. 301–314, 2009.
[30] H.Gu, H.Jiang, Z.Teng, Existence and global exponential stability of equilibrium of competitive neural networks with different time scales and multiple delays, Journal of the Franklin Institute, vol. 347, pp. 719–731, 2010.
[31] C.Li, J.Sun, R.Sun, Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects, Journal of the Franklin Institute, vol. 347, pp. 1186–1198, 2010.
[32] B.Boyd, et al, Linear Matrix Inequalities in Systmes and Control Theorem, SIAM, Philadelphia, 1994.