LMI Based Global Asymptotic Stability Criterion for Recurrent Neural Networks with Infinite Distributed Delays

Global asymptotic stability problem for a class of recurrent neural networks with infinite distributed delay is investigated based on the linear matrix inequality (LMI) technique. Using a matrix decomposition method, a vector-matrix form of recurrent neural networks with infinite distributed delay is obtained. Then by constructing a suitable Lyapunov functional and using an inequality, new LMI-based criteria are established to ensure the global asymptotic stability of the class of neural networks, which considers the effects of neuron's excitatory and inhibitory action in the term of infinite delay on the networks. The obtained results are independent of the size of delay and are easily verified. Numerical example shows the effectiveness of the obtained results.

[1]  Huaguang Zhang,et al.  Robust Exponential Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Shumin Fei,et al.  Simplified exponential stability analysis for recurrent neural networks with discrete and distributed time-varying delays , 2008, Appl. Math. Comput..

[3]  Shuping Bao,et al.  Exponential stability of reaction-diffusion Cohen-Grossberg neural networks with variable coefficients and distributed delays , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[4]  Yiguang Liu,et al.  On the Almost Periodic Solution of Cellular Neural Networks With Distributed Delays , 2007, IEEE Transactions on Neural Networks.

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

[6]  Q. Song,et al.  Global exponential stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2005 .

[7]  X. Liao,et al.  Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays , 2003 .

[8]  Jiye Zhang,et al.  Absolute stability of a class of neural networks with unbounded delay , 2004, Int. J. Circuit Theory Appl..

[9]  Wei Wu,et al.  Global exponential stability of Cohen-Grossberg neural networks with distributed delays , 2008, Neurocomputing.

[10]  Pagavathigounder Balasubramaniam,et al.  Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays , 2008 .

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

[12]  Jinde Cao,et al.  Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays , 2006 .

[13]  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.

[14]  Wei Wu,et al.  Global exponential stability of Cohen-Grossberg neural networks with distributed delays , 2008, Math. Comput. Model..

[15]  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.

[16]  Chuandong Li,et al.  Stability of Cohen-Grossberg neural networks with unbounded distributed delays , 2007 .

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

[18]  Wang,et al.  LMI-Based Criteria for Globally Asymptotic Stability of Cellular Neural Networks with Multiple Delays , 2007 .

[19]  Shuyong Li,et al.  Global exponential stability of Hopfield neural networks with distributed delays , 2009 .

[20]  Hongyong Zhao,et al.  Dynamical analysis of Cohen-Grossberg neural networks with distributed delays , 2007 .

[21]  Zhanshan Wang,et al.  Global Asymptotic Stability of Delayed Cellular Neural Networks , 2007, IEEE Transactions on Neural Networks.

[22]  Guangda Hu,et al.  Global exponential periodicity and stability of cellular neural networks with variable and distributed delays , 2008, Appl. Math. Comput..

[23]  Y. Chen.  Global asymptotic stability of delayed Cohen-Grossberg neural networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  X. Lou,et al.  On global exponential stability and existence of periodic solutions for BAM neural networks with distributed delays and reaction–diffusion terms , 2008 .

[25]  Qiang Zhang,et al.  Global exponential stability of Hopfield neural networks with continuously distributed delays , 2003 .

[26]  Jiye Zhang.  Absolute stability of a class of neural networks with unbounded delay: Research Articles , 2004 .

[27]  Derong Liu,et al.  On the global output convergence of a class of recurrent neural networks with time-varying inputs , 2005, Neural Networks.

[28]  Jianhua Sun,et al.  Global asymptotic stability of Cohen–Grossberg neural network with continuously distributed delays , 2005 .

[29]  Huaguang Zhang,et al.  Robust exponential stability analysis of neural networks with multiple time delays , 2007, Neurocomputing.

[30]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[31]  Yoshihiro Suda,et al.  Absolutely exponential stability of a class of neural networks with unbounded delay , 2004, Neural Networks.

[32]  Xuyang Lou,et al.  Global output convergence of Cohen–Grossberg neural networks with both time-varying and distributed delays , 2009 .

[33]  Jinde Cao,et al.  Global output convergence of recurrent neural networks with distributed delays , 2007 .

[34]  Eduard Feireisl,et al.  Attractors for semilinear damped wave equations on R 3 , 1994 .

[35]  Jun Wang,et al.  Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays , 2003 .