Exponential Stability Analysis for Uncertain Neural Networks with Discrete and Distributed Time-Varying Delays

This paper studies the problem of exponential stability analysis for uncertain neural networks with discrete and distributed time-varying delays. Together with a suitable augmented Lyapunov Krasovskii function, zero equalities, reciprocally convex approach and a novel sufficient condition to guarantee the exponential stability of the considered system. The several exponential stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

• Miaomiao Yang
• Shouming Zhong

• Exponential stability
• Uncertain Neural networks
• LMI approach
• Lyapunov-Krasovskii function
• Time-varying.

[1] S. Arik Daly,An analysis of exponential stability of delayed neural
networks with time-varying delays. Neural Networks.17(2004)
[2] R.Cau,C.Lien and J.W.Hsieh,Global exponential stability for uncertain
cellular neural networks with multiple time-varying delays via LMI
approach,Chaos Solitons Fractals 31(4)(2007) 1258-1267.
[3] H.J.Cho,J.H.Park,Novel delay-dependent robust stability criterion of
delayed cellular neural networks,Chaos Solitons Fractals 32(5)(2007)
1194C1200.
[4] H.Gu,H.Jiang and Z.Teng,Existence and global exponential stability of
equilibrium of competitive neural networks with different time-scales
and multiple delays,J.Franklin Inst.347(2010)719-731.
[5] Y.He,M.Wu,J.H.She,Delay-dependent exponential stability of delayed
neural networks with time-varyingdelays, IEEE Trans. Circuits Syst.II
Exp.Briefs 53 (7)(2006)553-557.
[6] Y.He,G.P.Liu,D.Rees,New delay-dependent stability criteria for
neutral networks with time-varying delays, IEEE Trans. Neural
Netw.18(1)(2007) 310-314.
[7] Phat,V.N.Trinh, H.(2010).Exponential stabilization of neural networks
with various activation functions and mixed time-varying delays.IEEE
Transactions on Neural Networks,21(7),1180-1184.
[8] Z.Zuo,C.Yang,Y Wang,A new method for stability analysis of recurrent
neural networks with interval time-varying delay,IEEE Trans.Neural
Networks 21(2)(2010)339-344.
[9] K.Gu,An integral inequality in the stability problem of time delay
systems,in: Proceedings of 39th IEEE Conference Decision Control,
2000, pp. 2805-2810.
[10] X.Zhu,Y.Wang,Delay-dependent exponential stability for the neural net
works with time-varying delays,Phys.LETTE.A 373(2009)4066-4072.
[11] Y.H.Du,S.M.Zhong,Exponential passivity of BAM neural networks
with time-varying delays.Applied Mathematics and Computation
221(2013)727-740.
[12] Boyd S,Ghaoui LE, Feron E, Balakrishnan V. Linear matrix inequalities
in system and control theory. Society for Industrial an Applied
Mathematics, PA:Philadelphia 1994.
[13] Q.Song,Z.Wang, Neural networks with discrete and distributed time
varying delays:a general stability analysis,Chaos Solitons Fract.37(2008)
1538-1547.
[14] C.Lien,L.Chung,Global asymptotic stability for cellular neural networks
with discrete and distributed time-varying delays, Chaos Solitons
Fract.34 (2007)1213-1219.
[15] T.Li,Q.Luo,C.Y.Sun,B.Y.Zhang, Exponential stability of recurrent neural
networks with time-varying discrete and distributed delays,Nonlinear
Anal. Real World Appl.10(2009)2581-2589.
[16] X. Zhu, Y. Wang, Delay-dependent exponential stability for neural
networks with discrete and distributed time-varying delays,Phys.Lett.A
373(2009) 4066-4072.
[17] J.K.Tian,S.M.Zhong,Y.Wang,Improved exponential stability criteri
for neural networks with time-varying delays,Neurocomputing
97(2012)164-173.
[18] L.Shi,H.Zhu,S.M.Zhong,Globally exponential stability criteria for neural
network with time-varying delays, Applied Mathematics Computation
219 10487-10498.