Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays

In this letter, the global asymptotic stability analysis problem is considered for a class of stochastic Cohen-Grossberg neural networks with mixed time delays, which consist of both the discrete and distributed time delays. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, a linear matrix inequality (LMI) approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square. It is shown that the addressed stochastic Cohen-Grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two LMIs are feasible, where the feasibility of LMIs can be readily checked by the Matlab LMI toolbox. It is also pointed out that the main results comprise some existing results as special cases. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria

[1]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[2]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  J J Hopfield,et al.  Neural computation by concentrating information in time. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[4]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[5]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[6]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[7]  T. Ens,et al.  Blind signal separation : statistical principles , 1998 .

[8]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[9]  Terrence J. Sejnowski,et al.  Blind source separation of more sources than mixtures using overcomplete representations , 1999, IEEE Signal Processing Letters.

[10]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[11]  Russell H. Lambert,et al.  OVERDETERMINED BLIND SOURCE SEPARATION: USING MORE SENSORS THAN SOURCE SIGNALS IN A NOISY MIXTURE , 2000 .

[12]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[13]  Raffaele Parisi,et al.  BLIND SOURCE SEPARATION IN NONLINEAR MIXTURES BY ADAPTIVE SPLINE NEURAL NETWORKS , 2001 .

[14]  Michael Zibulevsky,et al.  Underdetermined blind source separation using sparse representations , 2001, Signal Process..

[15]  T. Liao,et al.  Globally exponential stability of generalized Cohen–Grossberg neural networks with delays , 2003 .

[16]  Tianping Chen,et al.  Delay-independent stability analysis of Cohen-Grossberg neural networks , 2003 .

[17]  Jinde Cao,et al.  Boundedness and stability for Cohen–Grossberg neural network with time-varying delays☆ , 2004 .

[18]  Shigui Ruan,et al.  Dynamics of a two-neuron system with discrete and distributed delays , 2004 .

[19]  Yongkun Li.  Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays , 2004 .

[20]  Fabian J. Theis,et al.  Postnonlinear Overcomplete Blind Source Separation Using Sparse Sources , 2004, ICA.

[21]  James Lam,et al.  Stochastic stability analysis of fuzzy hopfield neural networks with time-varying delays , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[22]  Jianhua Sun,et al.  Mean square exponential stability of stochastic delayed Hopfield neural networks , 2005 .

[23]  Tianping Chen,et al.  Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions , 2005, Neural Networks.

[24]  S. Arik,et al.  Global stability analysis of Cohen–Grossberg neural networks with time varying delays , 2005 .

[25]  S. Arik.  Global robust stability analysis of neural networks with discrete time delays , 2005 .

[26]  Lin Wang,et al.  Stability of Cohen-Grossberg neural networks with distributed delays , 2005, Appl. Math. Comput..

[27]  Zidong Wang,et al.  On global asymptotic stability of neural networks with discrete and distributed delays , 2005 .

[28]  Jinde Cao,et al.  Global exponential stability of discrete-time Cohen-Grossberg neural networks , 2005, Neurocomputing.

[29]  Jianhua Sun,et al.  Global exponential stability and periodic solutions of Cohen–Grossberg neural networks with continuously distributed delays , 2005 .

[30]  Libin Rong.  LMI-based criteria for robust stability of Cohen–Grossberg neural networks with delay , 2005 .

[31]  David Luengo,et al.  A general solution to blind inverse problems for sparse input signals , 2005, Neurocomputing.

[32]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[33]  Zidong Wang,et al.  Robust stability analysis of generalized neural networks with discrete and distributed time delays , 2006 .