New global exponential stability criterion for neural networks with time-varying delay
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- 英文论文题名：New global exponential stability criterion for neural networks with time-varying delay
- 论文作者：Tang Hongji ; Han Yanwu ; Xiao Xiaoqing ; Pan Rui
- 英文论文作者：Tang Hongji ; Han Yanwu ; Xiao Xiaoqing ; Pan Rui ; School of science ; Nantong Univeristy ; School of Electronics and Information ; Nantong University
- 年：2017
- 作者机构：School of science,Nantong Univeristy;School of Electronics and Information,Nantong University;
- 英文论文关键词：Neural networks ; time-varying delay ; exponential stability ; Lyapunov-Krasovskii functional
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O175
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：222k
- 原文格式：D
- 会议级别：全国
摘要
This paper is concerned with global exponential stability problem for a class of neural networks with time-varying delays. An appropriate Lyaponov-krasovskii functional(LKF) is constructed firstly. The symmetric matrices involved in the LKF are not required to be all positive definite. The obtained criterion expressed in terms of linear matrix inequalities(LMIs)shows advantages over the existing ones since not only a novel LKF is constructed but also several techniques such as integral inequalities, convex combination technique, reciprocally convex technique and free matrix method are used to estimate the upper bound of the derivative of the LKF. Finally, two numerical examples are given to show the effectiveness and superiority of the obtained criterion.
This paper is concerned with global exponential stability problem for a class of neural networks with time-varying delays. An appropriate Lyaponov-krasovskii functional(LKF) is constructed firstly. The symmetric matrices involved in the LKF are not required to be all positive definite. The obtained criterion expressed in terms of linear matrix inequalities(LMIs)shows advantages over the existing ones since not only a novel LKF is constructed but also several techniques such as integral inequalities, convex combination technique, reciprocally convex technique and free matrix method are used to estimate the upper bound of the derivative of the LKF. Finally, two numerical examples are given to show the effectiveness and superiority of the obtained criterion.
This paper is concerned with global exponential stability problem for a class of neural networks with time-varying delays. An appropriate Lyaponov-krasovskii functional(LKF) is constructed firstly. The symmetric matrices involved in the LKF are not required to be all positive definite. The obtained criterion expressed in terms of linear matrix inequalities(LMIs)shows advantages over the existing ones since not only a novel LKF is constructed but also several techniques such as integral inequalities, convex combination technique, reciprocally convex technique and free matrix method are used to estimate the upper bound of the derivative of the LKF. Finally, two numerical examples are given to show the effectiveness and superiority of the obtained criterion.
引文
[1]D.Lin,J.Wu,J.Li,Less conservative stability condition for uncertain discrete-time recurrent neural networks with timevarying delays Neurocomputing,173:1578-1588,2016.
[2]Z.Wu,H.Su,J.Chu,W.Zhou,Improved delay dependent stability condition of discrete recurrent neural networks with time-varying delays.IEEE Trans.Neural Netw.,21(4):692-697,2010.
[3]Z.Wu,J.Lam,H.Su,J.Chu,Stability and dissipativity analysis of static neural networks with time delay,IEEE Trans.Neural Netw.Learn.Syst.,23(2):199-210,2012.
[4]D.Zhang,L.Yu,Exponential state estimation for Markovian jumping neural networks with time varying discrete and distributed delays,Neural networks,35(11):103-111,2012.
[5]H.Zeng,Y.He,M.Wu,H.Xiao,Improved condition for passivity of neural networks with time-varying delays.IEEE Trans.Cybem.,444(6):785-792,2014.
[6]O.M.Kwon,M.J.Park,S.M.Lee,J.H.Park,E.J.Cha,Stability for neural networks with time-varying delays via some new approaches,IEEE Trans.Neural Netw.Learning Syst.,24(2):181-193,2013.
[7]C.Zheng,H.Zhang,Z.Wang,Delay-dependent globally exponential stability criteria for static neural networks:an LMI approcah,IEEE Trans.Circuits Syst.II,56(7):605-609,2009.
[8]O.M.Kwon,M.J.Park,J.H.Park,S.M.Lee,E.J.Cha,On stability analysis for neural networks with interval timevarying delays via some new augmented Lyapunov-Krasovskii functional,Commun.Nonlinear Sci.Numer.Simul.,19(9):3184-3201,2014.
[9]O.M.Kwon,Ju H.Park,S.M.Lee,E.J.Cha,A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays,Applied Mathematics and Computation,217:10231-10238,2011.
[10]O.M.Kwon,M.J.Park,Ju H.Park,S.M.Lee,E.J.Cha,New and improved results on stability of static neural networks with interval time-varying delays,Applied Mathematics and Computation,239:346-357,2014.
[11]Y.He,Q.Wang,L.Xie,C.Lin,Further improvement of free weighting matrices technique for systems with time-varying delay.IEEE Transactions on Automatic Control,52(2):647-650,2007.
[12]H.Zeng,Y.He,M.Wu,C.Zhang,Complete delaydecomposing approach to asymptotic stability for neural networks with time-varying delays.IEEE Transactions on Neural Networks,22(5):806-812,2011.
[13]C.Ge,C.Hua,X.Guan,New delay-dependent stability criteria for neural networks with time-varying delay using delaydecomposition approach.IEEE Transactions on Neural Networks and Learning Systems,25(7):1378-1383,2014.
[14]H.Zhang,F.Yang,X.Liu,Q.Zhang,Stability analysis for neural networks with time-varying delay based on quadratic convex combination.IEEE Transactions on Neural Networks and Learning Systems,24(5):513-521,2013.
[15]M.Wu,F.Liu,P.Shi,Y.He,R.Yokoyama,Exponential stability analysis for neural networks with time-varying delay,IEEE Trans.Syst.,Man,Cybern.,B,Cybern.,38(4):1152-1156,2008.
[16]J.Xiao,Z.Zeng,A.Wu,New criteria for exponential stability of delayed recurrent neural networks,Neurocomputing,134:182-188,2014.
[17]M.Ji,Y.He,M.Wu,C.Zhang,Further results on exponential stability of neural networks with time-varying delay.Applied Mathematics and Computation,256:175-182,2015.
[18]Y.He,M.Ji,C.Zhang,M.Wu,Global exponential stability of neural networks with time-varying delay based on free-matrixbased integral inequality,Neural Networks,77:80-86,2016.
[19]R.Rakkiyappan,R.Sivasamy,Ju H.Park,Tae H.Lee,An improved stability criterion for generalized neural networks with additive time-varying delays,Neurocomputing,171:615-624,2016.
[20]Y.Liu,S.Lee,O.Kwon,J.Park,New approach to stability criteria for generalized neural networks with interval timevarying delays,Neurocomputing,149:1533-1551,2015.
[21]W.Peng,Q.Wu,Z.Zhang,LMI-based global exponential stability of equilibrium point for neutral delayed BAM neural networks with delays in leakage terms via new inequality technique,Neurocomputing,199:103-113,2016.
[22]B.Chen,J.Wang,Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time varying delays,Neural Netw.,20:1067-1080,2007.
[23]Y.He,M.Wu,J.She,Delay-dependent exponential stability of delayed neural networks with time-varying delay,IEEE Trans.Circuits Syst.II:Express Briefs,53:553-55,2006.
[24]X.Zhang,Q.Han,Global asymptotic stability for a class of generalized neural networks with interval time-varying delays.IEEE Transactions on Neural Networks,22(8):1180-1192,2011.
[25]M.Wu,F.Liu,P.Shi,Y.He,R.Yokoyama,Exponential stability analysis for neural networks with time-varying delays,IEEE Trans.Syst.Man Cybern.Part B,38:1152-1156,2008.
[26]Y.Wang,C.Yang,Z.Zuo,On exponential stability analysis for neural networks with time-varying delays and general activation functions,Commun.Nonlinear Sci.Numer.Simul.,17:1447-1459,2012.
[27]S.Zhu,Y.Shen,C.Chen,Exponential passivity of neural networks with time-varying delay and uncertainty,Physical Letters A,375:136-142,2010.
[28]H.Shao,Z.Zhang Delay-dependent state feedback stabilization for a networked control model with two additive input delays.Applied Mathematics and Computation,265:748-758,2015.
[29]P.Park,J.W.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays.Automatica,47(1):235-238,2011.
[30]A.Seuret,F.Gouaisbaut,Wirtinger-based integtal inequality:Application to time-delay systems.Automatica,49(9):2860-2866,2013.
[31]X.Liu,W.Yu,J.Cao,F.Alsaadi,Finite-time synchronisation control of complex networks via non-smooth analysis.IET Control Theory&Applications,9(8):1245-1253,2015.
[32]X.Liu,J.Cao,W Yu,Q Song,Nonsmooth finite-time synchronization of switched coupled neural networks.IEEE Trans.on Cybern.,46(10):2360-2371,2016.
[2]Z.Wu,H.Su,J.Chu,W.Zhou,Improved delay dependent stability condition of discrete recurrent neural networks with time-varying delays.IEEE Trans.Neural Netw.,21(4):692-697,2010.
[3]Z.Wu,J.Lam,H.Su,J.Chu,Stability and dissipativity analysis of static neural networks with time delay,IEEE Trans.Neural Netw.Learn.Syst.,23(2):199-210,2012.
[4]D.Zhang,L.Yu,Exponential state estimation for Markovian jumping neural networks with time varying discrete and distributed delays,Neural networks,35(11):103-111,2012.
[5]H.Zeng,Y.He,M.Wu,H.Xiao,Improved condition for passivity of neural networks with time-varying delays.IEEE Trans.Cybem.,444(6):785-792,2014.
[6]O.M.Kwon,M.J.Park,S.M.Lee,J.H.Park,E.J.Cha,Stability for neural networks with time-varying delays via some new approaches,IEEE Trans.Neural Netw.Learning Syst.,24(2):181-193,2013.
[7]C.Zheng,H.Zhang,Z.Wang,Delay-dependent globally exponential stability criteria for static neural networks:an LMI approcah,IEEE Trans.Circuits Syst.II,56(7):605-609,2009.
[8]O.M.Kwon,M.J.Park,J.H.Park,S.M.Lee,E.J.Cha,On stability analysis for neural networks with interval timevarying delays via some new augmented Lyapunov-Krasovskii functional,Commun.Nonlinear Sci.Numer.Simul.,19(9):3184-3201,2014.
[9]O.M.Kwon,Ju H.Park,S.M.Lee,E.J.Cha,A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays,Applied Mathematics and Computation,217:10231-10238,2011.
[10]O.M.Kwon,M.J.Park,Ju H.Park,S.M.Lee,E.J.Cha,New and improved results on stability of static neural networks with interval time-varying delays,Applied Mathematics and Computation,239:346-357,2014.
[11]Y.He,Q.Wang,L.Xie,C.Lin,Further improvement of free weighting matrices technique for systems with time-varying delay.IEEE Transactions on Automatic Control,52(2):647-650,2007.
[12]H.Zeng,Y.He,M.Wu,C.Zhang,Complete delaydecomposing approach to asymptotic stability for neural networks with time-varying delays.IEEE Transactions on Neural Networks,22(5):806-812,2011.
[13]C.Ge,C.Hua,X.Guan,New delay-dependent stability criteria for neural networks with time-varying delay using delaydecomposition approach.IEEE Transactions on Neural Networks and Learning Systems,25(7):1378-1383,2014.
[14]H.Zhang,F.Yang,X.Liu,Q.Zhang,Stability analysis for neural networks with time-varying delay based on quadratic convex combination.IEEE Transactions on Neural Networks and Learning Systems,24(5):513-521,2013.
[15]M.Wu,F.Liu,P.Shi,Y.He,R.Yokoyama,Exponential stability analysis for neural networks with time-varying delay,IEEE Trans.Syst.,Man,Cybern.,B,Cybern.,38(4):1152-1156,2008.
[16]J.Xiao,Z.Zeng,A.Wu,New criteria for exponential stability of delayed recurrent neural networks,Neurocomputing,134:182-188,2014.
[17]M.Ji,Y.He,M.Wu,C.Zhang,Further results on exponential stability of neural networks with time-varying delay.Applied Mathematics and Computation,256:175-182,2015.
[18]Y.He,M.Ji,C.Zhang,M.Wu,Global exponential stability of neural networks with time-varying delay based on free-matrixbased integral inequality,Neural Networks,77:80-86,2016.
[19]R.Rakkiyappan,R.Sivasamy,Ju H.Park,Tae H.Lee,An improved stability criterion for generalized neural networks with additive time-varying delays,Neurocomputing,171:615-624,2016.
[20]Y.Liu,S.Lee,O.Kwon,J.Park,New approach to stability criteria for generalized neural networks with interval timevarying delays,Neurocomputing,149:1533-1551,2015.
[21]W.Peng,Q.Wu,Z.Zhang,LMI-based global exponential stability of equilibrium point for neutral delayed BAM neural networks with delays in leakage terms via new inequality technique,Neurocomputing,199:103-113,2016.
[22]B.Chen,J.Wang,Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time varying delays,Neural Netw.,20:1067-1080,2007.
[23]Y.He,M.Wu,J.She,Delay-dependent exponential stability of delayed neural networks with time-varying delay,IEEE Trans.Circuits Syst.II:Express Briefs,53:553-55,2006.
[24]X.Zhang,Q.Han,Global asymptotic stability for a class of generalized neural networks with interval time-varying delays.IEEE Transactions on Neural Networks,22(8):1180-1192,2011.
[25]M.Wu,F.Liu,P.Shi,Y.He,R.Yokoyama,Exponential stability analysis for neural networks with time-varying delays,IEEE Trans.Syst.Man Cybern.Part B,38:1152-1156,2008.
[26]Y.Wang,C.Yang,Z.Zuo,On exponential stability analysis for neural networks with time-varying delays and general activation functions,Commun.Nonlinear Sci.Numer.Simul.,17:1447-1459,2012.
[27]S.Zhu,Y.Shen,C.Chen,Exponential passivity of neural networks with time-varying delay and uncertainty,Physical Letters A,375:136-142,2010.
[28]H.Shao,Z.Zhang Delay-dependent state feedback stabilization for a networked control model with two additive input delays.Applied Mathematics and Computation,265:748-758,2015.
[29]P.Park,J.W.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays.Automatica,47(1):235-238,2011.
[30]A.Seuret,F.Gouaisbaut,Wirtinger-based integtal inequality:Application to time-delay systems.Automatica,49(9):2860-2866,2013.
[31]X.Liu,W.Yu,J.Cao,F.Alsaadi,Finite-time synchronisation control of complex networks via non-smooth analysis.IET Control Theory&Applications,9(8):1245-1253,2015.
[32]X.Liu,J.Cao,W Yu,Q Song,Nonsmooth finite-time synchronization of switched coupled neural networks.IEEE Trans.on Cybern.,46(10):2360-2371,2016.