Global Asymptotic Stability and Robust Stability of a Class of Cohen–Grossberg Neural Networks With Mixed Delays

This paper is concerned with the global asymptotic stability of a class of Cohen-Grossberg neural networks with both multiple time-varying delays and continuously distributed delays. Two classes of amplification functions are considered, and some sufficient stability criteria are established to ensure the global asymptotic stability of the concerned neural networks, which can be expressed in the form of linear matrix inequality and are easy to check. Furthermore, some sufficient conditions guaranteeing the global robust stability are also established in the case of parameter uncertainties.

[1]  Tianping Chen,et al.  Global Asymptotical Stability of Cohen-Grossberg Neural Networks with Time-Varying and Distributed Delays , 2006, ISNN.

[2]  James Lam,et al.  Script H sign∞ model reduction of linear systems with distributed delay , 2005 .

[3]  Tianping Chen,et al.  Global exponential stability of delayed Hopfield neural networks , 2001, Neural Networks.

[4]  Lin Wang,et al.  Stability of Cohen-Grossberg neural networks with distributed delays , 2005, Appl. Math. Comput..

[5]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

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

[7]  Shangjiang Guo,et al.  Stability analysis of Cohen-Grossberg neural networks , 2006, IEEE Transactions on Neural Networks.

[8]  Lin Wang,et al.  Exponential stability of Cohen-Grossberg neural networks , 2002, Neural Networks.

[9]  S. Arik,et al.  Global stability analysis of Cohen–Grossberg neural networks with time varying delays , 2005 .

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

[11]  Qing-Long Han,et al.  On stability of recurrent neural networks-an approach from volterra integro-differential equations , 2006, IEEE Transactions on Neural Networks.

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

[13]  K. Tan,et al.  Dynamic stability conditions for Lotka-Volterra recurrent neural networks with delays. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

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

[16]  Jun Wang,et al.  Global exponential stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[17]  Tianping Chen,et al.  Rn+-global stability of a Cohen-Grossberg neural network system with nonnegative equilibria , 2007, Neural Networks.

[18]  Wang,et al.  Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Yuming Chen,et al.  Global stability of neural networks with distributed delays , 2002, Neural Networks.

[20]  Jinde Cao,et al.  Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays , 2005, Neural Networks.

[21]  Jinde Cao,et al.  Robust Stability of Switched Cohen–Grossberg Neural Networks With Mixed Time-Varying Delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[22]  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.

[23]  Daoyi Xu,et al.  Global attraction and stability for Cohen-Grossberg neural networks with delays , 2006, Neural Networks.

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

[25]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

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

[27]  Jinde Cao,et al.  Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays , 2006, IEEE Transactions on Neural Networks.

[28]  Jinde Cao,et al.  Global exponential stability of discrete-time Cohen-Grossberg neural networks , 2005, Neurocomputing.

[29]  Jinde Cao,et al.  An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[30]  Libin Rong LMI-based criteria for robust stability of Cohen–Grossberg neural networks with delay , 2005 .

[31]  Emilia Fridman,et al.  Robust H∞ control of distributed delay systems with application to combustion control , 2001, IEEE Trans. Autom. Control..

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

[33]  J. Lam,et al.  A delay-dependent approach to robust H/sub /spl infin// filtering for uncertain distributed delay systems , 2005, IEEE Transactions on Signal Processing.

[34]  Zhang Yi,et al.  Global convergence of Lotka-Volterra recurrent neural networks with delays , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[35]  X. Zou,et al.  Harmless delays in Cohen–Grossberg neural networks ☆ , 2002 .

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

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

[38]  M. Weihua Global Exponential Stability Analysis of Cohen-Grossberg Neural Networks , 2006 .

[39]  S. Niculescu Delay Effects on Stability: A Robust Control Approach , 2001 .

[40]  Lihua Xie,et al.  H/sub infinity / control and quadratic stabilization of systems with parameter uncertainty via output feedback , 1992 .

[41]  J. Hopfield Neurons withgraded response havecollective computational properties likethoseoftwo-state neurons , 1984 .

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

[43]  Jean-Pierre Richard,et al.  Stability of some linear systems with delays , 1999, IEEE Trans. Autom. Control..

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

[45]  L. Crocco Aspects of Combustion Stability in Liquid Propellant Rocket Motors Part I: Fundamentals. Low Frequency Instability With Monopropellants , 1951 .

[46]  Tianping Chen,et al.  Robust global exponential stability of Cohen-Grossberg neural networks with time delays , 2004, IEEE Transactions on Neural Networks.

[47]  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.

[48]  A. E. Pearson,et al.  A multistage reduction technique for feedback stabilizing distributed time-lag systems , 1987, Autom..

[49]  Mauro Forti,et al.  Generalized neural network for nonsmooth nonlinear programming problems , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[50]  Korris Fu-Lai Chung,et al.  Global exponential convergence of Cohen-Grossberg neural networks with time delays , 2005, IEEE Trans. Neural Networks.