New Approaches on Exponential Stability Analysis for Neural Networks with Time-Varying Delays
In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dependent exponential stability criteria are established in terms of LMIs and can be easily checked.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.
[1] M.T. Hagan, H.B. Demuth, M. Beale, Neural Network Design,PWS Publishing Company,Boston MA,1996.
[2] A. Cichoki, R. Unbehauen,Neural Networks for Optimization and Signal Processing, Wiley, Chichester,1993.
[3] J.D.Cao, L.Wang, Exponential stability and periodic oscillatory solution in BAM networks with delays,IEEE Trans. Neural Netw. 13(2002) 457-463.
[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] O.M.Kwon, J.H.Park, Improved delay-dependent stability criterion for networks with time-varying, Phys Lett. A 373(2009) 529-535.
[6] 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.
[7] S. Arik,Global asymptotic stability of hybrid bidirectional associative memory neural networks with time delays. Phys. Lett.A 351(2006) 85-91.
[8] 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.
[9] X. Zhu, Y. Wang, Delay-dependent exponential stability for neural networks with time-varying delays, Phys. Lett. A 373(2009) 4066-4027.
[10] P.G. Park, J.W. Ko, C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica 47(2011) 235-238.
[11] 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.
[12] 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.
[13] 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.
[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] 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.
[19] 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.
[20] 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.
[21] 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.
[22] 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.
[23] 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.
[24] 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.
[25] S. Cui, T. Zhao, J. Guo, Global robust exponential stability for interval neural networks with delay, Chaos Solitons Fractals 42 (3) (2009) 1567C1576.
[26] 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.
[27] 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.
[28] 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.
[29] O.M.Kwon, J.H.Park, Improved delay-dependent stability criterion for networks with time-varying, Phys Lett. A 373(2009) 529-535.
[30] 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.
[1] M.T. Hagan, H.B. Demuth, M. Beale, Neural Network Design,PWS Publishing Company,Boston MA,1996.
[2] A. Cichoki, R. Unbehauen,Neural Networks for Optimization and Signal Processing, Wiley, Chichester,1993.
[3] J.D.Cao, L.Wang, Exponential stability and periodic oscillatory solution in BAM networks with delays,IEEE Trans. Neural Netw. 13(2002) 457-463.
[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] O.M.Kwon, J.H.Park, Improved delay-dependent stability criterion for networks with time-varying, Phys Lett. A 373(2009) 529-535.
[6] 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.
[7] S. Arik,Global asymptotic stability of hybrid bidirectional associative memory neural networks with time delays. Phys. Lett.A 351(2006) 85-91.
[8] 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.
[9] X. Zhu, Y. Wang, Delay-dependent exponential stability for neural networks with time-varying delays, Phys. Lett. A 373(2009) 4066-4027.
[10] P.G. Park, J.W. Ko, C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica 47(2011) 235-238.
[11] 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.
[12] 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.
[13] 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.
[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] 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.
[19] 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.
[20] 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.
[21] 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.
[22] 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.
[23] 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.
[24] 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.
[25] S. Cui, T. Zhao, J. Guo, Global robust exponential stability for interval neural networks with delay, Chaos Solitons Fractals 42 (3) (2009) 1567C1576.
[26] 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.
[27] 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.
[28] 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.
[29] O.M.Kwon, J.H.Park, Improved delay-dependent stability criterion for networks with time-varying, Phys Lett. A 373(2009) 529-535.
[30] 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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:66468", author = "Qingqing Wang and Baocheng Chen and Shouming Zhong", title = "New Approaches on Exponential Stability Analysis for Neural Networks with Time-Varying Delays", abstract = "In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dependent exponential stability criteria are established in terms of LMIs and can be easily checked.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,Exponential stability, LMI approach, Time-varying delays.", volume = "8", number = "2", pages = "309-8", }
