Global Robust Attractive and Invariant Sets of Fuzzy Neural Networks with Delays and Impulses

A class of fuzzy neural networks (FNNs) with time-varying delays and impulses is investigated. With removing some restrictions on the amplification functions, a new differential inequality is established, which improves previouse criteria. Applying this differential inequality, a series of new and useful criteria are obtained to ensure the existence of global robust attracting and invariant sets for FNNs with time-varying delays and impulses. Our main results allow much broader application for fuzzy and impulsive neural networks with or without delays. An example is given to illustrate the effectiveness of our results.

[2]  Stanislaw H. Zak,et al.  On the Brain-State-in-a-Convex-Domain Neural Models , 1996, Neural Networks.

[3]  Huijun Gao,et al.  Robust Stability Criterion for Discrete-Time Uncertain Markovian Jumping Neural Networks With Defective Statistics of Modes Transitions , 2011, IEEE Transactions on Neural Networks.

[4]  Xinghuo Yu,et al.  A Unified Approach to the Stability of Generalized Static Neural Networks With Linear Fractional Uncertainties and Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Jun Wang,et al.  On the Stability of Globally Projected Dynamical Systems , 2000 .

[6]  Yuan Yan Tang,et al.  Guaranteed attractivity of Equilibrium Points in a Class of Delayed Neural Networks , 2006, Int. J. Bifurc. Chaos.

[7]  Qintao Gan,et al.  Exponential Synchronization of Stochastic Fuzzy Cellular Neural Networks with Reaction-Diffusion Terms via Periodically Intermittent Control , 2012, Neural Processing Letters.

[8]  Jinde Cao,et al.  Stability in static delayed neural networks: A nonlinear measure approach , 2006, Neurocomputing.

[9]  Peng Shi,et al.  Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[10]  Xinghua Wang,et al.  The existence and global attractivity of almost periodic sequence solution of discrete-time neural networks , 2006 .

[11]  Pineda,et al.  Generalization of back-propagation to recurrent neural networks. , 1987, Physical review letters.

[12]  L. B. Lmeida Backpropagation in perceptrons with feedback , 1988 .

[13]  Zhenkun Huang,et al.  Exponential p-stability of second order Cohen-Grossberg neural networks with transmission delays and learning behavior , 2007, Simul. Model. Pract. Theory.

[14]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[15]  Hongyong Zhao,et al.  Global asymptotic stability of Hopfield neural network involving distributed delays , 2004, Neural Networks.

[16]  L.O. Chua,et al.  Cellular neural networks , 1993, 1988., IEEE International Symposium on Circuits and Systems.

[17]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[18]  Yang Tang,et al.  Stability of delayed neural networks with time-varying impulses , 2012, Neural Networks.

[19]  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).

[20]  Ta-lun Yang,et al.  The global stability of fuzzy cellular neural network , 1996 .

[21]  Huijun Gao,et al.  Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts , 2010, IEEE Transactions on Signal Processing.

[22]  Yongkun Li Global exponential stability of BAM neural networks with delays and impulses , 2005 .

[23]  Daoyi Xu,et al.  Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays , 2006, Appl. Math. Comput..

[25]  Tingwen Huang,et al.  Global exponential estimates of delayed stochastic neural networks with Markovian switching , 2012, Neural Networks.

[26]  Daoyi Xu,et al.  Impulsive delay differential inequality and stability of neural networks , 2005 .

[27]  Xiaodi Li,et al.  LMI Approach for Stationary Oscillation of Interval Neural Networks With Discrete and Distributed Time-Varying Delays Under Impulsive Perturbations , 2010, IEEE Transactions on Neural Networks.

[28]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[29]  A. Michel,et al.  Analysis and synthesis of a class of neural networks: linear systems operating on a closed hypercube , 1989 .

[30]  Min Wang,et al.  Global asymptotic robust stability of static neural network models with S-type distributed delays , 2006, Math. Comput. Model..

[31]  Hong Qiao,et al.  A comparative study of two modeling approaches in neural networks , 2004, Neural Networks.

[32]  Hong Qiao,et al.  A reference model approach to stability analysis of neural networks , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[33]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[34]  Yongkun Li,et al.  Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses , 2013, Fuzzy Sets Syst..

[35]  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.

[36]  Jun Wang,et al.  A general methodology for designing globally convergent optimization neural networks , 1998, IEEE Trans. Neural Networks.