An LMI Approach to Stability Analysis of Reaction–Diffusion Cohen–Grossberg Neural Networks Concerning Dirichlet Boundary Conditions and Distributed Delays

The global asymptotic stability problem for a class of reaction-diffusion Cohen-Grossberg neural networks with both time-varying delay and infinitely distributed delay is investigated under Dirichlet boundary conditions. Instead of using the M-matrix method and the algebraic inequality method, under some suitable assumptions and using a matrix decomposition method, we adopt the linear matrix inequality method to propose two sufficient stability conditions for the concerned neural networks with Dirichlet boundary conditions and different kinds of activation functions, respectively. The obtained results are easy to check and improve upon the existing stability results. Two examples are given to demonstrate the effectiveness of the obtained results.

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

[2]  Zhanshan Wang,et al.  New Delay-Dependent Global Exponential Stability Criterion for Cellular-Type Neural Networks , 2009 .

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

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

[5]  Fang Liu,et al.  Exponential Stability Analysis for Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Qinghua Zhou,et al.  Exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays , 2008, Appl. Math. Comput..

[7]  Tianping Chen,et al.  New Conditions on Global Stability of Cohen-Grossberg Neural Networks , 2003, Neural Computation.

[8]  Daoyi Xu,et al.  Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays , 2003, Science in China Series F: Information Sciences.

[9]  Jeen-Shing Wang,et al.  A fully automated recurrent neural network for unknown dynamic system identification and control , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  Huaguang Zhang,et al.  New Delay-Dependent Global Exponential Stability Criterion for Cellular-Type Neural Networks With Time-Varying Delays , 2009, IEEE Trans. Circuits Syst. II Express Briefs.

[11]  Zhenjiang Zhao,et al.  Exponential periodicity and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays , 2006, Comput. Math. Appl..

[12]  Lihong Huang,et al.  Convergence dynamics of Cohen-Grossberg neural networks with continuously distributed delays , 2008, Appl. Math. Comput..

[13]  Huaguang Zhang,et al.  Robust Stability Analysis for Interval Cohen–Grossberg Neural Networks With Unknown Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[14]  Wei Wu,et al.  Analysis on global exponential robust stability of reaction–diffusion neural networks with S-type distributed delays , 2008 .

[15]  Huaguang Zhang,et al.  Global Asymptotic Stability and Robust Stability of a Class of Cohen–Grossberg Neural Networks With Mixed Delays , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Kunlun Wang,et al.  Dynamical behaviors of Cohen-Grossberg neural networks with delays and reaction-diffusion terms , 2006, Neurocomputing.

[17]  Chong Lin,et al.  Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays ☆ , 2009 .

[18]  Kelin Li,et al.  Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms , 2008, Neurocomputing.

[19]  Maohui Xia,et al.  LMI CONDITIONS FOR GLOBAL ASYMPTOTIC STABILITY OF NEURAL NETWORKS WITH DISCRETE AND DISTRIBUTED DELAYS , 2008 .

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

[21]  Zuoan Li,et al.  Stability analysis of impulsive Cohen-Grossberg neural networks with distributed delays and reaction-diffusion terms , 2009 .

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

[23]  Anthony W. Leung,et al.  Systems of Nonlinear Partial Differential Equations , 1989 .

[24]  S. Mohamad,et al.  Exponential stability preservation in discrete-time analogues of artificial neural networks with distributed delays , 2008 .

[25]  Jiye Zhang,et al.  Absolute stability analysis in cellular neural networks with variable delays and unbounded delay , 2004 .

[26]  Jinde Cao,et al.  Stability of Cohen-Grossberg neural networks with time-varying delays , 2007, Neural Networks.

[27]  Youshen Xia,et al.  A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[28]  Huaguang Zhang,et al.  Global Asymptotic Stability of Reaction–Diffusion Cohen–Grossberg Neural Networks With Continuously Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[29]  Shaocheng Tong,et al.  Adaptive neural network tracking control for a class of non-linear systems , 2010, Int. J. Syst. Sci..

[30]  Xinghua Wang,et al.  Exponential stability of impulsive Cohen–Grossberg networks with distributed delays , 2008 .

[31]  Alberto Tesei,et al.  Competition systems with Dirichlet boundary conditions , 1982 .

[32]  Huaguang Zhang,et al.  Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays , 2009, Neurocomputing.

[33]  Qing-Guo Wang,et al.  Delay-Dependent State Estimation for Delayed Neural Networks , 2006, IEEE Transactions on Neural Networks.

[34]  Jianhua Sun,et al.  Exponential stability of reaction–diffusion generalized Cohen–Grossberg neural networks with time-varying delays , 2007 .

[35]  Qing Zhu,et al.  Stability analysis on Cohen–Grossberg neural networks with both time-varying and continuously distributed delays☆ , 2009 .

[36]  Bing Chen,et al.  Mean square exponential stability of stochastic fuzzy Hopfield neural networks with discrete and distributed time-varying delays , 2009, Neurocomputing.

[37]  Jinde Cao,et al.  Global Synchronization in an Array of Delayed Neural Networks With Hybrid Coupling , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

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

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

[41]  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).

[42]  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 .

[43]  Huaguang Zhang,et al.  Delay-Dependent Guaranteed Cost Control for Uncertain Stochastic Fuzzy Systems With Multiple Time Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[44]  Xiaofeng Liao,et al.  Asymptotic stability of delayed neural networks: A descriptor system approach , 2009 .

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

[46]  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.

[47]  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).

[48]  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.

[49]  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.

[50]  Anthony W. Leung,et al.  Equilibria and stabilities for competing-species reaction-diffusion equations with Dirichlet boundary data , 1980 .

[51]  Chaojin Fu,et al.  Global Exponential Stability of Cohen-Grossberg Neural Networks with Reaction-Diffusion and Dirichlet Boundary Conditions , 2007, ICIC.

[52]  Huijun Gao,et al.  New Delay-Dependent Exponential Stability for Neural Networks With Time Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

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

[55]  Edgar N. Sánchez,et al.  Adaptive recurrent neural control for nonlinear system tracking , 2000, IEEE Trans. Syst. Man Cybern. Part B.

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

[58]  Jinde Cao,et al.  Impulsive Effects on Stability of Fuzzy Cohen–Grossberg Neural Networks With Time-Varying Delays , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[60]  Peng Shi,et al.  Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay , 2011, Neurocomputing.

[61]  Jinde Cao,et al.  Global asymptotic stability of bi-directional associative memory networks with distributed delays , 2004, Appl. Math. Comput..