Stochastic stability analysis of fuzzy hopfield neural networks with time-varying delays

The ordinary Takagi-Sugeno (TS) fuzzy models have provided an approach to represent complex nonlinear systems to a set of linear sub-models by using fuzzy sets and fuzzy reasoning. In this paper, stochastic fuzzy Hopfield neural networks with time-varying delays (SFVDHNNs) are studied. The model of SFVDHNN is first established as a modified TS fuzzy model in which the consequent parts are composed of a set of stochastic Hopfield neural networks with time-varying delays. Secondly, the global exponential stability in the mean square for SFVDHNN is studied by using the Lyapunov-Krasovskii approach. Stability criterion is derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages.

[1]  X. Mao,et al.  Stochastic Hopfield neural networks , 2003 .

[2]  Gonzalo Joya,et al.  Hopfield neural networks for optimization: study of the different dynamics , 2002 .

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

[4]  Pauline van den Driessche,et al.  Global Attractivity in Delayed Hopfield Neural Network Models , 1998, SIAM J. Appl. Math..

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

[6]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  Yong-Yan Cao,et al.  Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach , 2000, IEEE Trans. Fuzzy Syst..

[8]  Nasser M. Nasrabadi,et al.  Object recognition using multilayer Hopfield neural network , 1997, IEEE Trans. Image Process..

[9]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Xuerong Mao,et al.  RAZUMIKHIN-TYPE THEOREMS ON STABILITY OF STOCHASTIC NEURAL NETWORKS WITH DELAYS , 2001 .

[11]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[12]  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.

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

[14]  Xuerong Mao,et al.  Exponential stability and instability of stochastic neural networks 1 , 1996 .

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

[16]  Wen-Jing Li,et al.  Hopfield neural networks for affine invariant matching , 2001, IEEE Trans. Neural Networks.

[17]  Jixin Qian,et al.  Stability analysis for neural dynamics with time-varying delays , 1998, IEEE Trans. Neural Networks.