Mean Square Exponential Stability of Uncertain Stochastic Hopfield Neural Networks with Interval Time-Varying Delays

The problem of mean square exponential stability of uncertain stochastic Hopfield neural networks with interval time-varying delays is investigated in this paper. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the derivative of the delay function can exceed one. The uncertainties considered in this paper are norm-bounded and possibly time-varying. By Lyapunov-Krasovskii functional approach and stochastic analysis approach, a new delay-dependent stability criteria for the exponential stability of stochastic Hopfield neural networks is derived in terms of linear matrix inequalities(LMIs). A simulation example is given to demonstrate the effectiveness of the developed techniques.

[1]  P. Shi,et al.  Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties , 2008 .

[2]  Jinhui Zhang,et al.  New Robust Stability Criterion for Uncertain Fuzzy Systems with Fast Time-Varying Delays , 2006, FSKD.

[3]  Yuanqing Xia,et al.  A new global robust stability criteria for uncertain neural networks with fast time-varying delays , 2008 .

[4]  Ou Ou,et al.  Global robust exponential stability of delayed neural networks: An LMI approach , 2007 .

[5]  Huijun Gao,et al.  Novel Robust Stability Criteria for Stochastic Hopfield Neural Networks With Time Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Yurong Liu,et al.  Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays , 2006 .

[7]  Qing-Long Han,et al.  On Hinfinity control for linear systems with interval time-varying delay , 2005, Autom..

[8]  A. Selman.  Structure in Complexity Theory , 1986, Lecture Notes in Computer Science.

[9]  J. Qiu,et al.  New robust stability criteria for uncertain neural networks with interval time-varying delays , 2009 .

[10]  Kwok-Wo Wong,et al.  Global exponential stability for a class of generalized neural networks with distributed delays , 2004 .

[11]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Jinde Cao,et al.  Periodic solutions and its exponential stability of reaction–diffusion recurrent neural networks with continuously distributed delays , 2006 .

[13]  Jinhui Zhang,et al.  Robust Stability of Uncertain Linear Systems with Time-Varying Delay and Non-Linear Perturbations , 2006 .

[14]  X. Lou,et al.  Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters , 2007 .

[15]  Zidong Wang,et al.  Robust stability for stochastic Hopfield neural networks with time delays , 2006 .

[16]  S. Mohamad,et al.  Exponential stability in Hopfield-type neural networks with impulses , 2007 .

[17]  Qiankun Song,et al.  An analysis on existence and global exponential stability of periodic solutions for BAM neural networks with time-varying delays☆ , 2007 .

[18]  Zidong Wang,et al.  Exponential stability of delayed recurrent neural networks with Markovian jumping parameters , 2006 .

[19]  Vimal Singh,et al.  On global robust stability of interval Hopfield neural networks with delay , 2007 .