Delay-Dependent Stability Analysis for Neural Networks with Distributed Delays

This paper deals with the problem of delay-dependent
stability for neural networks with distributed delays. Some new
sufficient condition are derived by constructing a novel
Lyapunov-Krasovskii functional approach. The criteria are
formulated in terms of a set of linear matrix inequalities, this is
convenient for numerically checking the system stability using the
powerful MATLAB LMI Toolbox. Moreover, in order to show the
stability condition in this paper gives much less conservative results
than those in the literature, numerical examples are considered.





References:
[1] Y.Fang, T.G.Kincaid, Stability analysis of dynamical neural networks,
IEEE Trans. Neural Networks 7(1996) 996-1006.
[2] A.N.Michel, D.Liu, Qualitative Analysis and Synthesis of Recurrent
Neural Networks, Marcel Dekker,New York, 2002.
[3] L.O.Chua, CNN: A Paradigm for Complexity, World Scientific,
Singapore, 1998.
[4] J.H.Park,O.M.Kwon,Further results on state estimation for neural
networks of neutral-type with time-varying delay,App. Math. Comput.
208(2009) 69-57.
[5] Chen Y,Wu Y.Novel delay-dependent stability criteria of neural networks
with time-varying delay.Neurocomputing 2009;72:1065-70.
[6] X. Liu, C. Dang, Stability analysis of positive switched linear systems
with delays, IEEE Trans. Autom. Control 56(2011) 1684-1690.
[7] O.M. Kwon, J.H. Park, Delay-dependent stability for uncertain
cellular neural networks with discrete and distribute time-varying
delays,J.Franklin Inst. 345(2008) 766-778.
[8] Z.G. Wu, J.H. Park, H.Y. Su, J. Chu, New results on exponential
passivity of neural networks with time-varying delays, Nonlinear Anal.
Real World Appl. 13(2012) 1593-1599.
[9] S.M. Lee, O.M. Kwon, J.H. Park, A novel delay-dependent criterion
for delayed neural networks of neutral type, Phys. Lett. A 374(2010)
1843-1848.
[10] J.H. Park, O.M. Kwon, Synchronization of neural networks of neutral
type with stochastic perurbation, Mod. Phys. Lett. B 23(2009) 1743-
1751.
[11] Q. Song, Z. Wang,Neural networks with discrete and distributed
time-varying delays:a general stability analysis, Chaos Solitons Fract.
37(2008) 1538-1547.
[12] 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.
[13] Z.G. Wu, J.H. Park, H. Su, J.Chu, Dissipativity analysis for singular
systems with time-varying delays, Appl. Math. Comput. 218(2011)
4605-4613.
[14] S.Lakshmanan, Ju.H. Park, D.H.Ji, H.Y.Jung, G.Nagamani,State
estimation of neural networks with time-varying delays and Markovian
jumping parameter based on passivity theory, Nonlinear Dyn. 70(2012)
1421-1434.
[15] J. Chen,H. Zhu,S.M. Zhong, G.H. Li, Novel delay-dependent robust
stability criteria for neutral systems with mixed time-varying delays and
nonlinear perturbations, Appl. Math. Comput. 219(2013) 7741-7753.
[16] J.Cao, K.Yuan, H.X.Zou, Global asymptotical stability of recurrent
neural networks with multiple discrete delays and distributed delays,
IEEE Trans. Neural networks 17(2006)1646-1651.
[17] J.H.Park, Further result on asymptotic stability criterion of cellular
neural networks with multiple discrete and distributed delays,
Appl.Math.Comput. 182(2006)1661-1666.
[18] J.H.Park, An analysis of global robust stability of uncertain cellular
neural networks with discrete and distributed delays, Chaos Solitons
Fractals 32(2007)800-807.
[19] J. K. Tain, S.M. Zhong, New delay-dependent exponential stability
criteria for neural networks with discrete and distributed time-varying
delays, Neurocomputing 74 (2011) 3365-3375.
[20] Q.Song, J.Cao, Global exponential stability of bidirectional associative
memory neural networks with distributed delays, J.Comput. Appl. Math.
202(2006)266-279.
[21] W.-H.Chen, W.X. Zheng, Global asymptotic stability of a class of
neural networks with distributed delays,IEEE Trans. Circuits Syst.I
53(2007)644-652.
[22] S.Guo, L.Huang, Exponential stability and periodic solutions of
neural networks with continously distributed delays, Phys.Rev.E
67(2003)011902.
[23] C.Lin, Q.G.Wang,T.H.Lee, A less conservative robust stability test for
linear uncertain time-delay systems, IEEE Trans. Automat. Control
51(2006)87-91.
[24] K.Gu, V.L.Kharitonov, J.Chen, Stability of Time-Delay System,
Birkhauser, Boston, 2003.
[25] Liu PL. Robust exponential stability for uncertain time-varying delay
systems with delay dependence.Journal of The Franklin Institute
2009;346(10):958-968.
[26] R.E.Skeiton, T.lwasaki, K.M. Grigoradis, A Unified Algebraic Approach
to Linear Control Design, Taylor and Francis, New York, 1997.