Delay-Dependent Stability Analysis for Neural Networks with Distributed Delays
Authors: Qingqing Wang, Shouming Zhong
Abstract:
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.
Keywords: Neural networks, Globally asymptotic stability , LMI approach, Distributed delays.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1094043
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[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.