基于时滞分割技术的时滞神经网络系统时滞相依全局稳定性分析
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摘要
通过构造一个新的增广Lyapunov-Krasovskii泛函,利用时滞分割技术并结合自由权矩阵、Jensen积分不等式,得到一个时滞神经网络系统时滞相依全局渐近稳定新判据。该判据以LMI的形式给出,便于计算和验证。数值实例表明,文章结果改进了相关文献结论,具有更低的保守性。
In this paper, a delay-dependent stability sufficient condition was obtained by a newly constructed LyapunovKrasovskii functional together with delay fractioning technique, free weighing matrix method and Jensen integral inequality, which was in form of LMIs and was less conservative than the existing ones.
In this paper, a delay-dependent stability sufficient condition was obtained by a newly constructed LyapunovKrasovskii functional together with delay fractioning technique, free weighing matrix method and Jensen integral inequality, which was in form of LMIs and was less conservative than the existing ones.
引文
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[26]LI T,SONG A,XUE M,et al.Stability analysis on delayed neural networks based on an improved delay-partitioning approach[J].Journal of Computational and Applied Mathematics,2011,235:3086-3095.
[27]YANG R,GAO H,SHI P.Novel robust stability criteria for stochastic Hopfield neural networks with time delay[J].IEEE Transactions on Systems ManCybernetics.Part B Cybern,2009,39(2):467-474.
[28]YANG R,ZHANG Z,SHI P.Exponential stability on stochastic neural networks with discrete interval and distributed delays[J].IEEE Transactions on Neural Networks,2010,2(1):169-175.
[29]BOYD S,GHAUI L E,FERON E,et al.Linear matrix inequalities in system and control theory[M].Philadelphia:SIAM,1994:76-121.
[2]OZCAN N,ARIK S.Global robust stability analysis of neural networks with multiple time delays[J].IEEE Transactions on Circuits and System I,2006,35(1):166-176.
[3]PARK M J,KWON O M,PARK J H,et al.Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay[J].Applied Mathematics and Computation,2012,218:6762-6775.
[4]WU A L,ZENG Z G,ZHU X S,et al,Exponential synchronization of memristor-based recurrent neural networks with time delay[J].Neurocomputing,2011,24:3043-3050.
[5]YANG Y,CAO J D.Solving quadratic programming problems by delayed projection neural network[J].IEEETransactions on Neural Networks,2006,17:1630-1634.
[6]LI F.Delyed lagrangian neural networks for solving convex programming problems[J].Neurocomputing,2010,73:2266-2273.
[7]HE Y,LIU G P,REES D.New delay-dependent stability criteria for neural networks with time-varying delay[J].IEEE Transactions on Neural Networks,2007,18(1):310-314.
[8]HE Y,LIU G P,REES D.Stability analysis for neural networks with time-varying interval delay[J].IEEE Transactions on Neural Networks,2007,18(6):1850-1854.
[9]PARK JU H,CHO H J.A delay-dependent asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays[J].Chaos Sollitons Fractals,2007,33:436-442.
[10]PARK JU H,KWON O M.Further results on state estimation for neural networks of neutral-type with time-varying delay[J].Applied Mathematics and Computation,2009,208:69-75.
[11]SHAO J L,HUANG T Z,WANG X P.Further analysis on global robust exponential stability of neural networks with time-varying delay[J].Communications in Nonlinear Science and Numerical Simulation,2012,17:1117-1124.
[12]ZHANG Q,WEI X,XU J.Delay-dependent exponential stability cellular neural networks with time-varying delay[J].Chaos Sollitons Fractals,2005,23:1363-1369.
[13]SHAO H Y.Less conservative delay-dependent stability criteria for neural networks with time-varying delays[J].Neurocomputing,2010,73:1528-1532.
[14]MOU S,GAO H,QIANG W,et al.New delay-dependent exponential stability for neural networks with time delays[J].IEEE Transactions on Systems ManCybernetics:Part B Cybern,2008,38:571-576.
[15]LEE S M,KWON O M,PARK JU H.A novel delay-dependent criterion for delayed neural networks of neutral type[J].Physics Letter A,2010,374:1843-1848.
[16]MOU S,GAO H,LAM J,et al.A new criterion of delaydependent asymptotic stability for Hopfield neural networks with time delay[J].IEEE Transactions on Neural Networks,2008,19(3):532-534.
[17]ZHANG X,HAN Q.New Lyapunov-krasovskii functionals for global asymptotic stability of delayed neural networks[J].IEEE Transactions on Neural Networks,2008,20(3):533-539.
[18]DU B Z,LAM J.Stability analysis of static recurrent neural networks using delay-partitioning and projection[J].Neural Networks,2009,22:343-349.
[19]DU B Z,LAM J,SHU Z.A delay-partitioning projection approach to stability analysis of neutral systems[C]//Proceedings of the 17thWorld Congress,IFAC.2008:12348-12353.
[20]DU B Z,LAM J,SHU Z,et al.A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components[J].IET Control Theory and Application,2009,3(4):383-390.
[21]XIAO J,ZENG Z,WU A.New criteria for exponential stability of delayed recurrent neural networks[J].Neurocomputing,2014,134:182-188.
[22]HU L,GAO H,ZHENG W.Novel stability of cellular neural networks with interval time-varying delay[J].Neural Networks,2008,21:1458-1463.
[23]ZHANG Y,YUE D,TIAN E.New stability criteria of neural networks with interval time-varying delay:A piecewise delay method[J].Applied Mathematics and Computation,2009,208:249-259.
[24]LI T,SONG A,FEI S,et al.Delay derivative-dependent stability for delayed neural networks with unbounded distributed delay[J].IEEE Transactions on Neural Networks,2008,21(8):1365-1371.
[25]MENG X,LAM J,DU B,et al.A delay-partitioning approach to the stability analysis of discrete-time systems[J].Automatica,2010,46:610-614.
[26]LI T,SONG A,XUE M,et al.Stability analysis on delayed neural networks based on an improved delay-partitioning approach[J].Journal of Computational and Applied Mathematics,2011,235:3086-3095.
[27]YANG R,GAO H,SHI P.Novel robust stability criteria for stochastic Hopfield neural networks with time delay[J].IEEE Transactions on Systems ManCybernetics.Part B Cybern,2009,39(2):467-474.
[28]YANG R,ZHANG Z,SHI P.Exponential stability on stochastic neural networks with discrete interval and distributed delays[J].IEEE Transactions on Neural Networks,2010,2(1):169-175.
[29]BOYD S,GHAUI L E,FERON E,et al.Linear matrix inequalities in system and control theory[M].Philadelphia:SIAM,1994:76-121.