Exponential State Estimation for Neural Networks with Leakage, Discrete and Distributed Delays

In this paper, the design problem of state estimator for
neural networks with the mixed time-varying delays are investigated
by constructing appropriate Lyapunov-Krasovskii functionals and
using some effective mathematical techniques. In order to derive
several conditions to guarantee the estimation error systems to be
globally exponential stable, we transform the considered systems
into the neural-type time-delay systems. Then with a set of linear
inequalities(LMIs), we can obtain the stable criteria. Finally, three
numerical examples are given to show the effectiveness and less
conservatism of the proposed criterion.

• Liyuan Wang
• Shouming Zhong

• State estimator
• Neural networks
• Globally exponential stability.

[1] Y. Liu, Z. Wang, X. Liu, "Global exponential stsbility of generalized
recurrent neural networks with discrete and distributed delays,” Neural
Networks 19(2006)667-675.
[2] Y. Wang , Z. Wang , J. Liang ,"On robust stability of stochastic genetic
regulatory networks with time-delays : a delay fractioning papproach,”
IEEE Trans.Syst.Man Cybern.PartB 40(2010)729-740.
[3] X.Liu,"Delay-dependent H ∝ control for uncertain fuzzy systems with
time-varying delays,” Nonlinear Analysis:Theory,Methods Applications
68(2008)1352-1361.
[4] S. Y. Xu, Janmes Lam,"A new LMI condition for delay-dependent
asymptotic stability of delayed Hopfield neural networks,” IEEE Trans
Circuits Syst.53(2006)230-235.
[5] Y.He,M.Wu,"An improved global asymptotic stability criterion for
delayed cellular neural networks,” IEEE Trans, Neural Networks
17(2006)250-253.
[6] X.Y.Lou, B.T.Cui, "On the global robust asymptotic stability of
BAM neural networks with time-varying delays,” Neurocomputing
70(2006)273-279.
[7] W.H.Chen, X.M.Lu, "Delay-dependent exponential stability of neural
networks with variable delay” :An LMI approach,IEEE Trans.Circuits
Syst.53(2006)837-842.
[8] V.cingh,"Some remarks on global asympototic of neural networks with
constant delay,” Chaos Fractals 32(5)(2007)1720-1724.
[9] H.Huang,J.D.Cao."Exponential stability analysis of uncertain stochastic
neural networks with multiple delays.” Nonlinear Anal.8(2)(2007)646-
653.
[10] X.M.Zhang, M.Wu, J.H.she, "Delay-dependent stabilization of linear
systems with time-varying state and input delaays,” Automatica 41
(2005) 1405-1412.
[11] Z. Wang, D.W.C.Ho, X.Liu, " State estimation for delayed neural
networks,” IEEE Trans. Neural Netw.16 (2005)279C284.
[12] H.Wang,Q.Song," State estimation for neural networks with mixed
interval time-varying delays,” Neurocomputing. 73 (2010)1281-1288.
[13] H.Huang, G.Feng, J.Cao," An LMI approach to delay-dependent state
estimation for delayed neural networks,” Neurocomputing, 71 (2008)
2857-2867.
[14] T.Li,S.M.Fei,Q.Zhu,"Design of exponential state estimator for neural
networks with distributed delays,” Nonlinear Anal. Real World Appl.
10(2009)1229-1242.
[15] M.S. Mahmoud,"New exponentially convergent state estimation method
for delayed neural networks.” Neurocomputing, 72 (2009) 3935-3942.
[16] Z.Wang, Y.Liu, X.Liu, "State estimation for jumping recurrent neural
networks with discrete and distributed delays.” Neural Netw.22
(2009)41-48.
[17] P. Balasubramaniam,S. Lakshmanan Jeeva Sathya Theesar, S. Jeeva
Sathya Theesar, " State estimation for Markovian jumping recurrent neural
networks with interval time-varying delays.” Nonlinear Dynam.,60
(2009) 661-675.
[18] Y.Liu,Z.Wang,X.Liu,"Design of exponential state estimators for neural
networks with mixed time delays.” Phys.Lett.A, 364 (2007) 401-412.
[19] C. K. Ahn. "Delay-dependent state estimation for T-S fuzzy delayed
Hopfield neural networks,” Nonlinear Dynam.61 (2010)483-489.
[20] Y.Chen,W.Bi,W.Li,Y.Wu,"Less conservative results of state estimation
for neural networks with time-varying delay.” Neurocomputing,73
(2010) 1324-1331.
[21] J.H.Park,O.M.Kwon,"Design of state estimator for neural networks of
neutral-type.” Appl. Math. Comput.202(2008)360-369
[22] Lin Shi, Hong Zhu, Shouming Zhong, Liyuan Hou, " Globally
exponential stability for neural networks with time-varying delays.”
Applied Mathematics and Computation 219 (2013) 10487-10498.
[23] K.Gu,"An integral inequality in the stability promblem of time delay
systems,” in:Proceedings of 39th IEEE Conference Decision Control,
2000.2805-2810.
[24] O.M.Kwon,J.H.Park,S.M.Lee,"An improved delay-dependent criterion
for asymptotic stability of uncertain dynamic systems with time-varying
delays,” J.Optim.Theory Appl.Math.Comput.218(2012)6762-6775.
[25] S.Lakshmannan, Ju H. Park, H.Y.Jung, "Design of state estimator for
neural networks with leakage,discrete and distributed delays,” Applied
Mathematices and computation 218 (2012) 11297-11310.
[26] H.wang,Q.song, " state estimation for neural networks with mixed
interval time-varying delays,” Neuromputing 73(2010)1281-1288.
[27] T.Li,S.M.Fei,Q.Zhu, "Design of exponential state estimator for neural
networks with distributed delays,” Nonlinear Anal.Real World Appl.
10(2009)1229-1242.
[28] Y.Liu,Z.Wang,X.Liu, "Design of exponential state estimators for neural
networks with mixed time delay,” Phys.Lett,A 364(2007)401-412.
[29] Y.Chen, W.Bi, W.Li, Y.Wu, "Less conservation result of state estimation
for neural networks with time-varying delay,” Neurocomputing 73
(2010) 1324-1331.
[30] Y,R.Liu,Z.D.Wang,X.H.Liu, "Design of exponential state estimators for
neural networks with mixed time delays,” Phys.Lett.A 364(5)(2007)401-
412.
[31] P.Gahinet,A.Nemirovsky,A.J.Lau,M.Chilali,LMI Control Toolbox:For
Use with Matlab,The MATH Works Inc,1995.
[32] Z.D.Wang,Daniel W.C.Ho,X.H.Liu, "State estimation for delayed neural
networks,” IEEE Trans.Neural Netw.16(1)(2005)279-284.
[33] Y.He, Q.G.Wang, M.Wu, C.Lin, "Delay-dependent state estimation for
delayed neural networks,” IEEE Trans, Neural Netw, 17 (4) (2006) 1077-
1081.
[34] Tao.Li,Shu-min Fei,Qing Zhu, "Design of exponential stste estimator
for neural networks with distributed delays,” Nonlinear Analysis:Real
World Applications 109(2009)1229-1242.
[35] C.Corduneanu,Principles of Differential and Integral Equations,Allyn
and Bacon,Boston,1971.