Robust Exponential Stability of Uncertain Stochastic Neural Networks With Distributed Delays and Reaction-Diffusions

This paper considers the problem of stability analysis for uncertain stochastic neural networks with distributed delays and reaction-diffusions. Two sufficient conditions for the robust exponential stability in the mean square of the given network are developed by using a Lyapunov-Krasovskii functional, an integral inequality, and some analysis techniques. The conditions, which are expressed by linear matrix inequalities, can be easily checked. Two simulation examples are given to demonstrate the reduced conservatism of the proposed conditions.

[1]  Qi Luo,et al.  Stabilization of stochastic Hopfield neural network with distributed parameters , 2004, Science in China Series F: Information Sciences.

[2]  Derong Liu,et al.  Cloning template design of cellular neural networks for associative memories , 1997 .

[3]  X. Lou,et al.  Global asymptotic stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2006 .

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

[5]  Jinde Cao,et al.  Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances , 2011, IEEE Transactions on Neural Networks.

[6]  Junguo Lu Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions , 2008 .

[7]  Jinde Cao,et al.  Global stability analysis in delayed cellular neural networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Min Wu,et al.  Stability Analysis for Neural Networks With Time-Varying Interval Delay , 2007, IEEE Transactions on Neural Networks.

[9]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[10]  Chuangxia Huang,et al.  Stability Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Time-Varying Delays , 2009 .

[11]  Frank L. Lewis,et al.  Neural Network Control Of Robot Manipulators And Non-Linear Systems , 1998 .

[12]  Shengyuan Xu,et al.  Passivity analysis for uncertain BAM neural networks with time delays and reaction–diffusions , 2013, Int. J. Syst. Sci..

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

[14]  Jinde Cao,et al.  Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays , 2003 .

[15]  Zhidong Teng,et al.  Impulsive Control and Synchronization for Delayed Neural Networks With Reaction–Diffusion Terms , 2010, IEEE Transactions on Neural Networks.

[16]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[17]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .

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

[19]  Jun Wang,et al.  Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks , 2002, IEEE Trans. Autom. Control..

[20]  Xiaofeng Liao,et al.  Robust Stability and Robust Periodicity of Delayed Recurrent Neural Networks With Noise Disturbance , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[21]  K. Gopalsamy,et al.  Stability in asymmetric Hopfield nets with transmission delays , 1994 .

[22]  Yang Shuzi,et al.  Stability of general neural networks with reaction-diffusion , 2001 .

[23]  Wei Xing Zheng,et al.  Global asymptotic stability of a class of neural networks with distributed delays , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Shengyuan Xu,et al.  Improved global robust asymptotic stability criteria for delayed cellular neural networks , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  Huaguang Zhang,et al.  An LMI Approach to Stability Analysis of Reaction–Diffusion Cohen–Grossberg Neural Networks Concerning Dirichlet Boundary Conditions and Distributed Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[27]  Guoping Liu,et al.  On-line identification of nonlinear systems using volterra polynomial basis function neural networks , 1997, 1997 European Control Conference (ECC).

[28]  Zhigang Zeng,et al.  Design and Analysis of High-Capacity Associative Memories Based on a Class of Discrete-Time Recurrent Neural Networks , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[29]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[30]  Jun-Guo Lu,et al.  Robust Global Exponential Stability for Interval Reaction–Diffusion Hopfield Neural Networks With Distributed Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[31]  James Lam,et al.  A New Criterion of Delay-Dependent Asymptotic Stability for Hopfield Neural Networks With Time Delay , 2008, IEEE Transactions on Neural Networks.

[32]  L. Pinneo On noise in the nervous system. , 1966, Psychological review.

[33]  Jianhua Sun,et al.  Convergence dynamics of stochastic reaction–diffusion recurrent neural networks with continuously distributed delays☆ , 2008 .

[34]  D. Williams STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS , 1976 .

[35]  Tunc Geveci,et al.  Advanced Calculus , 2014, Nature.

[36]  Jun Peng,et al.  Delay-independent stability of stochastic reaction–diffusion neural networks with Dirichlet boundary conditions , 2010, Neural Computing and Applications.

[37]  Gene A. Tagliarini,et al.  Optimization Using Neural Networks , 1991, IEEE Trans. Computers.

[38]  Linshan Wang,et al.  Global exponential robust stability of reaction¿diffusion interval neural networks with time-varying delays , 2006 .

[39]  F. Deng,et al.  Stabilization of stochastic Hopfield neural network with distributed parameters , 2004, Science in China Series F: Information Sciences.

[40]  Hong Qiao,et al.  Nonlinear measures: a new approach to exponential stability analysis for Hopfield-type neural networks , 2001, IEEE Trans. Neural Networks.

[41]  Shuzi Yang,et al.  Stability of general neural networks with reaction-diffusion , 2007, Science in China Series : Information Sciences.