Robust stability of discrete-time stochastic neural networks with time-varying delays

In this paper, the global exponential stability problem is studied for a class of discrete-time uncertain stochastic neural networks with time delays. The stability analysis problem is investigated, for the first time, for such kind of neural networks. In the neural network model, the parameter uncertainties are norm-bounded, the neural networks are subjected to stochastic disturbances described in terms of a Brownian motion, and the delay is time-varying. By utilizing a Lyapunov-Krasovskii functional and using some well-known inequalities, we convert the addressed stability analysis problem into the feasibility problem of several linear matrix inequalities (LMIs). Different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to establish sufficient conditions for the neural networks to be globally, robustly, exponentially stable. A numerical example is provided to show the usefulness of the proposed global stability condition.

[1]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

[2]  Guanrong Chen,et al.  New criteria for synchronization stability of general complex dynamical networks with coupling delays , 2006 .

[3]  A. R. Humphries,et al.  Dynamical Systems And Numerical Analysis , 1996 .

[4]  Giuliano Grossi.  A Discrete Adaptive Stochastic Neural Model for Constrained Optimization , 2006, ICANN.

[5]  A. G. Naim,et al.  Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks , 2002 .

[6]  Dewen Hu,et al.  Stability and bifurcation analysis on a discrete-time neural network , 2005 .

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

[8]  Jinde Cao,et al.  Discrete-time bidirectional associative memory neural networks with variable delays , 2005 .

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

[10]  Igor Pospelov,et al.  Inefficient equilibria in transition economy , 1999 .

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

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

[13]  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.

[14]  Lisheng Wang,et al.  Sufficient and necessary conditions for global exponential stability of discrete-time recurrent neural networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Zidong Wang,et al.  Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis , 2007 .

[16]  K. Shanti Swarup,et al.  Neural computation using discrete and continuous Hopfield networks for power system economic dispatch and unit commitment , 2006, Neurocomputing.

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

[18]  Enrique Mérida Casermeiro,et al.  Hebbian Iterative Method for Unsupervised Clustering with Automatic Detection of the Number of Clusters with Discrete Recurrent Networks , 2005, CAEPIA.

[19]  Wu-Hua Chen,et al.  Global exponential stability for discrete-time neural networks with variable delays , 2006 .

[20]  James Lam,et al.  Robust energy-to-peak filter design for stochastic time-delay systems , 2006, Syst. Control. Lett..

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

[22]  Jinde Cao,et al.  Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays , 2006 .

[23]  Jun Wang,et al.  Global robust stability of a class of discrete-time interval neural networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Lin Zou,et al.  Periodic solutions for nonautonomous discrete-time neural networks , 2006, Appl. Math. Lett..

[25]  Jinde Cao,et al.  Convergence of Discrete-Time Recurrent Neural Networks with Variable Delay , 2005, Int. J. Bifurc. Chaos.

[26]  Hsin-Chieh Chen,et al.  Image-processing algorithms realized by discrete-time cellular neural networks and their circuit implementations , 2006 .

[27]  Lei Wang,et al.  Stability and bifurcation for discrete-time Cohen-Grossberg neural network , 2006, Appl. Math. Comput..

[28]  S. Arik.  Stability analysis of delayed neural networks , 2000 .

[29]  K. Gopalsamy,et al.  Exponential stability of continuous-time and discrete-time cellular neural networks with delays , 2003, Appl. Math. Comput..

[30]  Hongjun Xiang,et al.  Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks , 2006 .

[31]  Hongjun Xiang,et al.  EXISTENCE AND GLOBAL STABILITY OF PERIODIC SOLUTION FOR DELAYED DISCRETE HIGH-ORDER HOPFIELD-TYPE NEURAL NETWORKS , 2005 .

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