Exponential Stability of Neural Networks with Time Delays

journal6 ›› 2008, Vol. 29 ›› Issue (4): 30-34.

• Mathematics • Previous Articles Next Articles

Exponential Stability of Neural Networks with Time Delays

(Department of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047,China)

Online:2008-07-25 Published:2012-05-21
About author:YANG De-gang (1976-),male,was born in Zigong City,Sichuan Province,associate professor of Chongqing Normal University;research areas are neural networks,nonlinear dynamical systems and network security.
Supported by:
Supported by the NSFC (60573047);Natural Science Foundation Project of CQ CSTC (2006BB2254,2007BB2231);Applying Basic Research Program of Chongqing Education Committee (KJ060818);Doctoral Foundation Project of Chongqing Normal University (08XLB003)

Abstract

Abstract: This paper considers the problems of global exponential stability for a general class of neural networks with time delays,a new criterion ensuring global exponential stability is obtained by utilizing Razumikhin theorem and the linear matrix inequality (LMI) technique.Distinct difference from other analytical approaches lies in “linearization” of the neural network model,by which the considered neural network model is transformed into a linear time-variant system.The obtained conditions show to be less conservative and restrictive.A numerical simulation is given to illustrate the validity of our results.

Key words: neural networks, time delays, exponential stability, linear matrix inequality, Razumikhin theorem

YANG De-Gang. Exponential Stability of Neural Networks with Time Delays[J]. journal6, 2008, 29(4): 30-34.

References

[1]CAO Jin-de.Periodic Oscillation and Exponential Stability of Delayed CNNs [J].Physics Letters A,2002,270(2-4):157-163.

[2]ARIK S.Stability Analysis of Delayed Neural Networks [J].IEEE Transactions on Circuits Systems I，2000,47(7):1 089-1 092.

[3]MOHAMAD S,GOPALSAMY K.Exponential Stability of Continuous-Time and Discrete-Time Cellular Neural Networks with Delays [J].Applied Mathematics and Computation，2003,135(1):17-38.

[4]LU Hong-tao,SHEN Rui-ming,CHUNG FU LAI.Global Exponential Convergence of Cohen-Grossberg Neural Networks with Time Delays [J].IEEE Transactions on Neural Networks,2005,16(6):1 694-1 696.

[5]LIAO Xiao-feng,CHEN Guan-rong,SANCHEZ E N.Delay-Dependent Exponential Stability Analysis of Delayed Neural Networks:An LMI Approach [J].Neural Networks，2002,15:855-866.

[6]LI Chuan-dong,LIAO Xiao-feng.Delay-Dependent Exponential Stability Analysis of Bi-Directional Associative Memory Neural Networks:An LMI Approach [J].Chaos,Solitons & Fractals,2005,24(4):1 119-1 134.

[7]LI Chuan-dong,LIAO Xiao-feng.New Algebraic Conditions for Global Exponential Stability of Delayed Recurrent Neural Networks [J].Neurocomputing,2005(64):319-333.

[8]QIAO Hong,PENG Ji-gen,XU Zong-ben.Nonlinear Measures:A New Approach toExponential Stability Analysis for Hopfield-Type Neural Networks [J].IEEE TNN,2001(12):360-370.

[9]LU Hong-tao,CHEN Guan-rong.Global Exponential Convergence of Multitime-Scale Neural Networks [J].IEEE Transactions on Circuits and Systems II:Express Briefs，2005,52(11):761-765.

[10]SANCHEZ E N,PEREZ J P.Input-to-State Stability Analysis for Dynamic NN [J].IEEE Transactions on Circuits Systems I，1999，46:1 895-1 398.

[11]BOYD S,GHAOUI L,FERON EI E，et al.Linear Matrix Inequalities in Systems and Control Theory [M].Philadephia:SIAM,1994.

[12]GU Ke-qin,CHEN Jie,KHARITONOV VLADIMIR L.Stability of Time-Delay System [M].New York：Springer-Verlag,2003.

[1]	PENG Chunyuan, SHEN Changchun. Reachable Set Estimation for Generalized Semi-Markov Jump Systems [J]. Journal of Jishou University(Natural Sciences Edition), 2023, 44(2): 17-23.
[2]	ZHANG Xipan, SHEN Changchun. Reachable Set Boundary Estimation for Neutral Markovian Jump Systems [J]. Journal of Jishou University(Natural Sciences Edition), 2023, 44(2): 7-16.
[3]	WANG Yu, ZHANG Shiru, ZHANG Yuji, ZHOU Liqun. Global Polynomial Stabilization of Proportional Delayed Neural Networks [J]. Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 15-25.
[4]	WANG Jun. Medium and Long Term Power Load Prediction in an Area of Anhui Province [J]. Journal of Jishou University（Natural Sciences Edition), 2018, 39(6): 46-49.
[5]	LIU Xiao-Lei, MA Cui-Ling, HAO Shu-Yan. Mittag-Leffler Stability of a Class of Fractional Order Hopfield Neural Networks [J]. journal6, 2015, 36(5): 21-26.
[6]	LUO Yi. Analysis and Prediction on the Chaotic Property of Traffic Flow Time Series [J]. journal6, 2013, 34(5): 60-65.
[7]	KANG Wei, LI Lin-Guo. Stability of Stochastic Neural Networks with Discrete and Distributed Time-Varying Delays [J]. journal6, 2012, 33(4): 37-40.
[8]	SONG Jiang-Yan, LIU Ping, LI Yong-Kun. Anti-Periodic Solutions for a Class of Neural Networks with Variable and Unbounded Time Delays [J]. journal6, 2009, 30(4): 23-29.
[9]	WANG Lian-Gui, LI Sen. Stability Analysis and Control for a Class of Switched Systems with Time-Delay [J]. journal6, 2008, 29(5): 49-52.
[10]	HUANG Gan, CAO Jin-De. Robust State Estimation for Uncertain Neural Networks [J]. journal6, 2008, 29(2): 30-34.
[11]	XIE Chang-Yan, HE Yi-Gang. Eliminating Missed Diagnosis in Fault Location for Nonlinear Resistance Networks [J]. journal6, 2006, 27(6): 53-55.
[12]	JIANG Li-Qun. Existence and Globally Exponential Stability of Periodic Solutions for Neural Networks with Delays [J]. journal6, 2006, 27(1): 32-38.
[13]	XIE Guang-Jun. Quantum Neural Computation Technology [J]. journal6, 2005, 26(1): 3-7.
[14]	ZHU Zhi-Qiang, CHEN Chao-Tian. Partial Connective Stability of Large-Scale Systems With Functionally Dependent Factory [J]. journal6, 2002, 23(3): 47-51.

Exponential Stability of Neural Networks with Time Delays

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 14

Recommended Articles

Metrics

Comments