Improved Exponential Stability Criteria for Recurrent Neural Networks with Time-varying Discrete and Distributed Delays

Yuan-Yuan Wu; Tao Li; Yu-Qiang Wu

doi:10.1007/s11633-010-0199-z

May 2010

Article Contents

Yuan-Yuan Wu, Tao Li and Yu-Qiang Wu. Improved Exponential Stability Criteria for Recurrent Neural Networks with Time-varying Discrete and Distributed Delays. International Journal of Automation and Computing, vol. 7, no. 2, pp. 199-204, 2010. doi: 10.1007/s11633-010-0199-z

Cite as: Yuan-Yuan Wu, Tao Li and Yu-Qiang Wu. Improved Exponential Stability Criteria for Recurrent Neural Networks with Time-varying Discrete and Distributed Delays. International Journal of Automation and Computing, vol. 7, no. 2, pp. 199-204, 2010. doi: 10.1007/s11633-010-0199-z

Improved Exponential Stability Criteria for Recurrent Neural Networks with Time-varying Discrete and Distributed Delays

1.
School of Automation, Southeast University, Nanjing 210096, PRC;
2.
Department of Information and Communication, Nanjing University of Information Science and Technology, Nanjing 210044, PRC;
3.
Institute of Automation, Qufu Normal University, Qufu 273165, PRC

Author Biography:

Yuan-Yuan Wu received her B.Sc.and M.Sc.degrees from the College of Mathematics and Information at Henan Normal University,Xinxiang,PRC in 2003 and 2006,respectivelyd
Corresponding author: Yu-Qiang Wu received the Ph.D.degree in automatic control from Southeast University,Nanjing,PRC in 1994

Received: 2008-10-23

Fund Project:

supported by National Natural Science Foundation of China (No.60674027,No.60974127);Key Project of Education Ministry of China (No.208074)

Abstract

In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks (RNNs) with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.
- Neural networks,
- time-varying delay,
- exponential stability,
- linear matrix inequalities (LMIs)

References

[1]	T.Li,Q.Luo,C.Y.Sun,B.Y.Zhang.Exponential stability of recurrent neural networks with time-varying discrete and distributed delays.Nonlinear Analysis:Real World Appli-cations,vol.10,no.4,pp.2581-2589,2009.
[2]	K.Ma,L.Yu,W.A.Zhang.Global exponential stabil-ity of cellular neural networks with time-varying discrete and distributed delays.Neurocomputing,vol.72,no.10- 12,pp.2705-2709,2009.
[3]	J.Yu,K.Zhang,S.Fei,T.Li.Simplified exponential sta-bility analysis for recurrent neural networks with discrete and distributed time-varying delays.Applied Mathematics and Computation,vol.205,no.1,pp.465-474,2008.
[4]	T.Li,S.Fei.Exponential state estimation for recurrent neural networks with distributed delays.Neurocomputing, vol.71,no.1-3,pp.428-438,2007.
[5]	Z.Wang,Y.Liu,X.Liu.On global asymptotic stability of neural networks with discrete and distributed delays. Physics Letters A,vol.345,no.4-6,pp.299-308,2005.
[6]	J.H.Park,H.J.Cho.A delay-dependent asymptotic stabil-ity criterion of cellular neural networks with time-varying discrete and distributed delays.Chaos,Solitons and Frac-tals,vol.33,no.2,pp.436-442,2007.
[7]	Z.Wang,H.Shu,Y.Liu,D.W.C.Ho,X.Liu.Robust sta-bility analysis of generalized neural networks with discrete and distributed time delays.Chaos,Solitons and Fractal, vol.30,no.4,pp.886-896,2006.
[8]	C.C.Hua,C.N.Long,X.P.Guan.New results on sta-bility analysis of neural networks with time-varying delays. Physics Letters A,vol.352,no.4-5,pp.335-340,2006.
[9]	S.Y.Xu,J.Lam,D.W.C.Ho,Y.Zou.Novel global asymp-totic stability criteria for delayed cellular neural networks. IEEE Transactions on Circuits and Systems II:Express Briefs,vol.52,no.6,pp.349-353,2005.
[10]	Y.G.Chen,W.P.Bi.New robust exponential stability analysis for uncertain neural networks with time-varying delay.International Journal of Automation and Comput-ing,vol.5,no.4,pp.395-400,2008.
[11]	Y.He,M.Wu,J.H.She.Delay-dependent exponential stability of delayed neural networks with time-varying de-lay.IEEE Transactions on Circuits and Systems II:Express Briefs,vol.53,no.7,pp.553-557,2006.
[12]	M.Wu,F.Liu,P.Shi,Y.He,R.Yokoyama.Exponential stability analysis for neural networks with time-varying de-lay.IEEE Transactions on Systems,Man,and Cybernetics, vol.38,no.4,pp.1152-1156,2008.
[13]	X.Y.Lou,B.T.Cui.Delay-dependent criteria for robust stability of uncertain switched Hopfield neural networks.In-ternational Journal of Automation and Computing,vol.4, no.3,pp.304-314,2007.
[14]	Y.Y.Wu,Y.Q.Wu,Y.G.Chen.Mean square exponen-tial stability of uncertain stochastic neural networks with time-varying delay.Neurocomputing,vol.72,no.10-12, pp.2379-2384,2009.

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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Improved Exponential Stability Criteria for Recurrent Neural Networks with Time-varying Discrete and Distributed Delays

1. School of Automation, Southeast University, Nanjing 210096, PRC;

2. Department of Information and Communication, Nanjing University of Information Science and Technology, Nanjing 210044, PRC;

3. Institute of Automation, Qufu Normal University, Qufu 273165, PRC

Corresponding author: Yu-Qiang Wu received the Ph.D.degree in automatic control from Southeast University,Nanjing,PRC in 1994

Received: 2008-10-23

Fund Project:

supported by National Natural Science Foundation of China (No.60674027,No.60974127);Key Project of Education Ministry of China (No.208074)

Key words:

Abstract: In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks (RNNs) with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.

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Reference (14)

[1]	T.Li,Q.Luo,C.Y.Sun,B.Y.Zhang.Exponential stability of recurrent neural networks with time-varying discrete and distributed delays.Nonlinear Analysis:Real World Appli-cations,vol.10,no.4,pp.2581-2589,2009.
[2]	K.Ma,L.Yu,W.A.Zhang.Global exponential stabil-ity of cellular neural networks with time-varying discrete and distributed delays.Neurocomputing,vol.72,no.10- 12,pp.2705-2709,2009.
[3]	J.Yu,K.Zhang,S.Fei,T.Li.Simplified exponential sta-bility analysis for recurrent neural networks with discrete and distributed time-varying delays.Applied Mathematics and Computation,vol.205,no.1,pp.465-474,2008.
[4]	T.Li,S.Fei.Exponential state estimation for recurrent neural networks with distributed delays.Neurocomputing, vol.71,no.1-3,pp.428-438,2007.
[5]	Z.Wang,Y.Liu,X.Liu.On global asymptotic stability of neural networks with discrete and distributed delays. Physics Letters A,vol.345,no.4-6,pp.299-308,2005.
[6]	J.H.Park,H.J.Cho.A delay-dependent asymptotic stabil-ity criterion of cellular neural networks with time-varying discrete and distributed delays.Chaos,Solitons and Frac-tals,vol.33,no.2,pp.436-442,2007.
[7]	Z.Wang,H.Shu,Y.Liu,D.W.C.Ho,X.Liu.Robust sta-bility analysis of generalized neural networks with discrete and distributed time delays.Chaos,Solitons and Fractal, vol.30,no.4,pp.886-896,2006.
[8]	C.C.Hua,C.N.Long,X.P.Guan.New results on sta-bility analysis of neural networks with time-varying delays. Physics Letters A,vol.352,no.4-5,pp.335-340,2006.
[9]	S.Y.Xu,J.Lam,D.W.C.Ho,Y.Zou.Novel global asymp-totic stability criteria for delayed cellular neural networks. IEEE Transactions on Circuits and Systems II:Express Briefs,vol.52,no.6,pp.349-353,2005.
[10]	Y.G.Chen,W.P.Bi.New robust exponential stability analysis for uncertain neural networks with time-varying delay.International Journal of Automation and Comput-ing,vol.5,no.4,pp.395-400,2008.
[11]	Y.He,M.Wu,J.H.She.Delay-dependent exponential stability of delayed neural networks with time-varying de-lay.IEEE Transactions on Circuits and Systems II:Express Briefs,vol.53,no.7,pp.553-557,2006.
[12]	M.Wu,F.Liu,P.Shi,Y.He,R.Yokoyama.Exponential stability analysis for neural networks with time-varying de-lay.IEEE Transactions on Systems,Man,and Cybernetics, vol.38,no.4,pp.1152-1156,2008.
[13]	X.Y.Lou,B.T.Cui.Delay-dependent criteria for robust stability of uncertain switched Hopfield neural networks.In-ternational Journal of Automation and Computing,vol.4, no.3,pp.304-314,2007.
[14]	Y.Y.Wu,Y.Q.Wu,Y.G.Chen.Mean square exponen-tial stability of uncertain stochastic neural networks with time-varying delay.Neurocomputing,vol.72,no.10-12, pp.2379-2384,2009.

Improved Exponential Stability Criteria for Recurrent Neural Networks with Time-varying Discrete and Distributed Delays

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