Stability Analysis of Neural Networks with Leakage, Discrete and Distributed Delays
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Stability Analysis of Neural Networks with Leakage, Discrete and Distributed Delays

Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

This paper deals with the problem of stability of neural networks with leakage, discrete and distributed delays. A new Lyapunov functional which contains some new double integral terms are introduced. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay system, and by making use of some inequality techniques, delay-dependent criteria are developed to guarantee the stability of the considered system. Finally, numerical examples are provided to illustrate the usefulness of the proposed main results.

Keywords: Neural networks, Stability, Time-varying delays, Linear matrix inequality.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1091396

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[1] Q.K. Song, Z.J. Zhao, Y.M. Li, Global exponential stability of BAM neural networks with distributed delays and reaction diffusion terms, Phys. Lett.A 335(2005) 213-225.
[2] F.Long,S.Fei,Z.Fu,H∞ control and quadratic stabilization of switched linear systems with linear fractional uncertainties via output feedback,Nonlinear Anal:Hybrid Syst.2(2008) 18-27.
[3] O.M.Kwon, J.H.Park, Improved delay-dependent stability criterion for networks with time-varying, Phys Lett. A 373(2009) 529-535.
[4] D. Lin, X. Wang, Self-organizing adaptive fuzzy neural control for the synchronization of uncertain chaotic systems with random-varying parameters, Neurocomputing 74 (12C13) (2011) 2241C2249.
[5] J.L. Wang, H.N. Wu, Robust stability and robust passivity of parabolic complex networks with parametric uncertainties and time-varying delays, Neurocomputing 87 (2012) 26C32.
[6] 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.
[7] S. Cui, T. Zhao, J. Guo, Global robust exponential stability for interval neural networks with delay, Chaos Solitons Fractals 42 (3) (2009) 1567C1576.
[8] O.M.Kwon,Ju H.Park,Exponential stability analysis for uncertain neural networks with interval time-varying delays.Applied Mathematics and Computation 212(2009) 530-541.
[9] P.G.Park, J.W.Ko, C.Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47(2011)235-238.
[10] D.Yue, C. Peng, G. Y. Tang, Guaranteed cost control of linear systems over networks with state and input quantizations, IEE Proc. Control Theory Appl. 153 (6) (2006) 658-664.
[11] 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.
[12] 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.
[13] L.Shi,H.Zhu,S.M.Zhong,L.Y.Hou,Globally exponential stability for neural networks with time-varying delays,Applied Mathematics and Computation 219(2013) 10487-10498.
[14] 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.
[15] J.H. Park, O.M. Kwon, Synchronization of neural networks of neutral type with stochastic perurbation, Mod. Phys. Lett. B 23(2009) 1743- 1751.
[16] Q. Song, Z. Wang,Neural networks with discrete and distributed time-varying delays:a general stability analysis, Chaos Solitons Fract. 37(2008) 1538-1547.
[17] 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.
[18] M.T. Hagan, H.B. Demuth, M. Beale, Neural Network Design,PWS Publishing Company,Boston MA,1996.
[19] A. Cichoki, R. Unbehauen,Neural Networks for Optimization and Signal Processing, Wiley, Chichester,1993.
[20] J.D.Cao, L.Wang, Exponential stability and periodic oscillatory solution in BAM networks with delays,IEEE Trans. Neural Netw. 13(2002) 457- 463.
[21] 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.
[22] O.M.Kwon, J.H.Park, Improved delay-dependent stability criterion for networks with time-varying, Phys Lett. A 373(2009) 529-535.
[23] Q.K. Song, Z.J. Zhao, Y.M. Li, Global exponential stability of BAM neural networks with distributed delays and reaction diffusion terms, Phys. Lett.A 335(2005) 213-225.
[24] S. Arik,Global asymptotic stability of hybrid bidirectional associative memory neural networks with time delays. Phys. Lett.A 351(2006) 85- 91.
[25] X.F. Liao, G. Chen, E.N.Sanchez, Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach, Neural Netw. 15(2002) 855-866.
[26] X. Zhu, Y. Wang, Delay-dependent exponential stability for neural networks with time-varying delays, Phys. Lett. A 373(2009) 4066-4027.
[27] P.G. Park, J.W. Ko, C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica 47(2011) 235-238.
[28] O.M.Kwon,J.H.Park,S.M.Lee,On robust stability for uncertain neural networks with interval time-vary delays,IET Control Theory and Applications 7(2008)625-634.
[29] O.M.Kwon,Ju H.Park,Exponential stability analysis for uncertain neural networks with interval time-varying delays.Applied Mathematics and Computation 212(2009)530-541.
[30] 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.