article

Global asymptotic stability and robust stability of a class of Cohen-Grossberg neural networks with mixed delays

Authors:

Huaguang Zhang,

Derong LiuAuthors Info & Claims

IEEE Transactions on Circuits and Systems Part I: Regular Papers, Volume 56, Issue 3

Pages 616 - 629

https://doi.org/10.1109/TCSI.2008.2002556

Published: 01 March 2009 Publication History

Abstract

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.

References

[1]

S. Arik and Z. Orman, "Global stability analysis of Cohen-Grossberg neural networks with time varying delays," Phys. Lett. A, vol. 341, no. 5/6, pp. 410-421, 2005.

[2]

S. Boyd, L. G. El, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, ser. Studies in Applied Mathematics. Philadelphia, PA: SIAM, 1994, vol. 15.

[3]

J. Cao, K. Yuan, and H. X. Li, "Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays," IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1646-1651, Nov. 2006.

Digital Library

[4]

T. Chen, "Global exponential stability of delayed Hopfield neural networks," Neural Netw., vol. 14, no. 8, pp. 977-980, Oct. 2001.

Digital Library

[5]

T. Chen and L. Rong, "Delay-independent stability analysis of Cohen-Grossberg neural networks," Phys. Lett. A, vol. 317, no. 5/6, pp. 436-449, Oct. 2003.

[6]

T. Chen and W. Lu, "Global asymptotical stability of Cohen-Grossberg neural networks with time-varying and distributed delays," Proc. Int. Symp. Neural Netw., ser. Lecture Notes in Computer Science, vol. 3971, pp. 192-197, 2006.

[7]

T. Chen and L. Rong, "Robust global exponential stability of Cohen-Grossberg neural networks with time delays," IEEE Trans. Neural Netw., vol. 15, no. 1, pp. 203-206, Jan. 2004.

Digital Library

[8]

W.-H. Chen and W. Zheng, "Global asymptotic stability of a class of neural networks with distributed delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 3, pp. 644-652, Mar. 2006.

[9]

Y. Chen, "Global stability of neural networks with distributed delays," Neural Netw., vol. 15, no. 7, pp. 867-871, Sep. 2002.

Digital Library

[10]

Y. Chen, "Global asymptotic stability of delayed Cohen-Grossberg neural networks," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 2, pp. 351-357, Feb. 2006.

[11]

M. A. Cohen and S. Grossberg, "Absolute stability and global pattern formation and parallel memory storage by competitive neural networks," IEEE Trans. Syst., Man, Cybern., vol. SMC-13, no. 5, pp. 815-826, Sep./Oct. 1983.

[12]

L. Crocco, "Aspect of combustion stability in liquid propellant rocket motors, Part I: Fundamentals of low frequency instability with monopropellants," J. Amer. Rocket Soc., vol. 21, no. 2, pp. 163-178, Feb. 1951.

[13]

Y. A. Fiagbedzi and A. E. Pearson, "A multistage reduction technique for feedback stabilizing distributed time-lag systems," Automatica, vol. 23, no. 3, pp. 311-326, May 1987.

Digital Library

[14]

M. Forti and A. Tesi, "New conditions for global stability of neural networks with application to linear and quadratic programming problems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42, no. 7, pp. 354-366, Jul. 1995.

[15]

M. Forti, P. Nistri, and M. Quincampoix, "Generalized neural network for nonsmooth nonlinear programming problems," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 9, pp. 1741-1754, Sep. 2004.

[16]

M. Forti, P. Nistri, and D. Papini, "Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain," IEEE Trans. Neural Netw., vol. 16, no. 6, pp. 1449-1463, Nov. 2005.

Digital Library

[17]

K. Gopalsamy and X. He, "Stability in asymmetric Hopfield nets with transmission delays," Phys. D, Nonlinear Phenomena, vol. 76, no. 4, pp. 344-358, Sep. 1994.

Digital Library

[18]

K. Gopalsamy and X. He, "Delay-independent stability in bidirectional associative neural networks," IEEE Trans. Neural Netw., vol. 5, no. 6, pp. 998-1002, Nov. 1994.

Digital Library

[19]

S. Guo and L. Huang, "Stability analysis of Cohen-Grossberg neural networks," IEEE Trans. Neural Netw., vol. 17, no. 1, pp. 106-116, Jan. 2006.

Digital Library

[20]

J. J. Hopfield, "Neurons with graded response have collective computational properties like those of two-stage neurons," Proc. Nat. Acad. Sci. USA, vol. 81, no. 10, pp. 3088-3092, May 1984.

[21]

H. Huang, D. W. C. Ho, and J. D. Cao, "Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays," Neural Netw., vol. 18, no. 2, pp. 161-170, Mar. 2005.

Digital Library

[22]

V. B. Kolmanovskii and J.-P. Richard, "Stability of some linear systems with delays," IEEE Trans. Autom. Control, vol. 44, no. 5, pp. 984-989, May 1999.

[23]

J. Lam, H. Gao, and C. Wang, "H _∞ model reduction of linear systems with distributed delay," Proc. Inst. Elect. Eng.-Control Theory Appl., vol. 152, no. 6, pp. 662-674, Nov. 2005.

[24]

X. X. Liao and J. Wang, "Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 2, pp. 268-275, Feb. 2003.

[25]

P. Liu and Q.-L. Han, "On stability of recurrent neural networks--An approach from Volterra integro-differential equations," IEEE Trans. Neural Netw., vol. 17, no. 1, pp. 264-267, Jan. 2006.

Digital Library

[26]

H. Lu, "Global exponential stability analysis of Cohen-Grossberg neural networks," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 52, no. 9, pp. 476-479, Aug. 2005.

[27]

H. Lu, R. Shen, and F.-L. Chung, "Global exponential convergence of Cohen-Grossberg neural networks with time delays," IEEE Trans. Neural Netw., vol. 16, no. 6, pp. 1694-1696, Nov. 2005.

Digital Library

[28]

K. Lu, D. Xu, and Z. Yang, "Global attraction and stability for Cohen-Grossberg neural networks with delays," Neural Netw., vol. 19, no. 10, pp. 1538-1549, Dec. 2006.

Digital Library

[29]

W. Lu and T. Chen, "New conditions on global stability of Cohen-Grossberg neural networks," Neural Comput., vol. 15, no. 5, pp. 1173-1189, May 2003.

Digital Library

[30]

W. Lu and T. Chen, "R₊ ⁿ global stability of Cohen-Grossberg neural network system with nonnegative equilibria," Neural Netw., vol. 20, no. 6, pp. 714-722, Aug., 2007.

[31]

S. I. Niculosu, Delay Effects on Stability-A Robust Control Approach. London, U.K.: Springer-Verlag, 2001.

[32]

J. P. Richard, "Time-delay system: An overview of some recent advances and open problems," Automatica, vol. 39, no. 10, pp. 1667-1694, Oct. 2003.

Digital Library

[33]

L. Rong, "LMI-based criteria for robust stability of Cohen-Grossberg neural networks with delay," Phys. Lett. A, vol. 339, no. 1/2, pp. 63-73, May 2005.

[34]

L. Wang, "Stability of Cohen-Grossberg neural networks with distributed delays," Appl. Math. Comput., vol. 160, no. 1, pp. 93-110, Jan. 2005.

Digital Library

[35]

L. Wang and X. Zou, "Harmless delays in Cohen-Grossberg neural network," Phys. D, Nonlinear Phenomena, vol. 170, no. 2, pp. 162-173, Sep. 2002.

[36]

L. Wang and X. Zou, "Exponential stability of Cohen-Grossberg neural networks," Neural Netw., vol. 15, no. 3, pp. 415-422, Apr. 2002.

Digital Library

[37]

Z. Wang, H. Zhang, and W. Yu, "Robust exponential stability analysis of neural networks with multiple time delays," Neurocomputing, vol. 70, no. 13-15, pp. 2534-2543, Aug. 2007.

Digital Library

[38]

L. Xie, E. Fridman, and U. Shaked, "Robust H _∞ control of distributed delay systems with application to combustion control," IEEE Trans. Autom. Control, vol. 46, no. 12, pp. 1930-1935, Dec. 2001.

[39]

L. Xie, M. Fu, and C. E. de Souza, "H _∞ control and quadratic stabilization of system with parameter uncertainty via output feedback," IEEE Trans. Autom. Control, vol. 37, no. 8, pp. 1253-1256, Aug. 1992.

[40]

W. Xiong and J. Cao, "Global exponential stability of discrete-time Cohen-Grossberg neural networks," Neurocomputing, vol. 64, pp. 433-446, Mar. 2005.

Digital Library

[41]

S. Xu, J. Lam, T. Chen, and Y. Zou, "A delay-dependent approach to robust H _∞ filtering for uncertain distributed delay systems," IEEE Trans. Signal Process., vol. 53, no. 10, pp. 3764-3772, Oct. 2005.

Digital Library

[42]

H. Ye, A. N. Michel, and K. Wang, "Qualitative analysis of Cohen-Grossberg neural networks with multiple delays," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 51, no. 3, pp. 2611-2618, Mar. 1995.

[43]

Z. Yi and K. K. Tan, "Dynamic stability conditions for Lotka-Volterra recurrent neural networks with delays," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 66, no. 1, p. 011 910, Jul. 2002.

[44]

Z. Yi and K. K. Tan, "Global convergence of Lotka-Volterra recurrent neural networks with delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 11, pp. 2482-2489, Nov. 2005.

[45]

K. Yuan and J. Cao, "An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 9, pp. 1854-1861, Sep. 2005.

[46]

K. Yuan, J. Cao, and H. X. Li, "Robust stability of switched Cohen-Grossberg neural networks with mixed time-varying delays," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 36, no. 6, pp. 1356-1363, Dec. 2006.

[47]

Z. Zeng, J. Wang, and X. X. Liao, "Global exponential stability of a general class of recurrent neural networks with time-varying delays," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 10, pp. 1353-1358, Oct. 2003.

[48]

H. Zhang and Z. Wang, "Global asymptotic stability of delayed cellular neural networks," IEEE Trans. Neural Netw., vol. 18, no. 3, pp. 947-950, May 2007.

Digital Library

[49]

H. Zhang, Z. Wang, and D. Liu, "Robust exponential stability of recurrent neural networks with multiple time-varying delays," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 54, no. 8, pp. 730-734, Aug. 2007.

[50]

H. Zhang, Z. Wang, and D. Liu, "Global asymptotic stability of recurrent neural networks with multiple time-varying delays," IEEE Trans. Neural Netw., vol. 19, no. 5, pp. 855-873, May 2008.

Digital Library

Cited By

Aktas EFaydasicok OArik S(2023)Robust stability of dynamical neural networks with multiple time delays: a review and new resultsArtificial Intelligence Review10.1007/s10462-023-10552-x56:Suppl 2(1647-1684)Online publication date: 1-Nov-2023
https://dl.acm.org/doi/10.1007/s10462-023-10552-x
Chen WHuang YRen S(2018)Passivity and synchronization of coupled reactiondiffusion CohenGrossberg neural networks with state coupling and spatial diffusion couplingNeurocomputing10.1016/j.neucom.2017.09.063275:C(1208-1218)Online publication date: 31-Jan-2018
https://dl.acm.org/doi/10.1016/j.neucom.2017.09.063
Cui NJiang HHu CAbdurahman A(2018)Global asymptotic and robust stability of inertial neural networks with proportional delaysNeurocomputing10.1016/j.neucom.2017.07.001272:C(326-333)Online publication date: 10-Jan-2018
https://dl.acm.org/doi/10.1016/j.neucom.2017.07.001
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Index Terms

Global asymptotic stability and robust stability of a class of Cohen-Grossberg neural networks with mixed delays
1. Computing methodologies
  1. Machine learning
    1. Machine learning approaches
      1. Neural networks
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

Index terms have been assigned to the content through auto-classification.

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cover image IEEE Transactions on Circuits and Systems Part I: Regular Papers

IEEE Transactions on Circuits and Systems Part I: Regular Papers Volume 56, Issue 3

March 2009

190 pages

ISSN:1549-8328

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IEEE Press

Publication History

Published: 01 March 2009

Revised: 02 December 2007

Received: 23 June 2007

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Cited By

Aktas EFaydasicok OArik S(2023)Robust stability of dynamical neural networks with multiple time delays: a review and new resultsArtificial Intelligence Review10.1007/s10462-023-10552-x56:Suppl 2(1647-1684)Online publication date: 1-Nov-2023
https://dl.acm.org/doi/10.1007/s10462-023-10552-x
Chen WHuang YRen S(2018)Passivity and synchronization of coupled reactiondiffusion CohenGrossberg neural networks with state coupling and spatial diffusion couplingNeurocomputing10.1016/j.neucom.2017.09.063275:C(1208-1218)Online publication date: 31-Jan-2018
https://dl.acm.org/doi/10.1016/j.neucom.2017.09.063
Cui NJiang HHu CAbdurahman A(2018)Global asymptotic and robust stability of inertial neural networks with proportional delaysNeurocomputing10.1016/j.neucom.2017.07.001272:C(326-333)Online publication date: 10-Jan-2018
https://dl.acm.org/doi/10.1016/j.neucom.2017.07.001
Bao GZeng Z(2018)Stability Analysis for Memristive Recurrent Neural Network Under Different External StimulusNeural Processing Letters10.1007/s11063-017-9671-x47:2(601-618)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1007/s11063-017-9671-x
Lakshmanan SLim CPrakash MNahavandi SBalasubramaniam P(2017)Neutral-type of delayed inertial neural networks and their stability analysis using the LMI ApproachNeurocomputing10.1016/j.neucom.2016.12.020230:C(243-250)Online publication date: 22-Mar-2017
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(2016)New delay-decomposing approaches to stability criteria for delayed neural networksNeurocomputing10.1016/j.neucom.2015.12.088189:C(123-129)Online publication date: 12-May-2016
https://dl.acm.org/doi/10.1016/j.neucom.2015.12.088
Zhou CZeng XYu JJiang H(2016)A unified associative memory model based on external inputs of continuous recurrent neural networksNeurocomputing10.1016/j.neucom.2015.12.079186:C(44-53)Online publication date: 19-Apr-2016
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Samli R(2015)A new delay-independent condition for global robust stability of neural networks with time delaysNeural Networks10.1016/j.neunet.2015.03.00466:C(131-137)Online publication date: 1-Jun-2015
https://dl.acm.org/doi/10.1016/j.neunet.2015.03.004
Song QZhao ZLiu Y(2015)Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delaysNeurocomputing10.1016/j.neucom.2015.05.020168:C(1044-1050)Online publication date: 30-Nov-2015
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Samli RYucel E(2015)Global robust stability analysis of uncertain neural networks with time varying delaysNeurocomputing10.1016/j.neucom.2015.04.058167:C(371-377)Online publication date: 1-Nov-2015
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