具有混合时变时滞主从神经网络的指数采样同步控制
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摘要
对于具有混合时变时滞的主从神经网络指数采样同步控制问题,运用Lyapunov-Krasovskii泛函方法以及线性矩阵不等式方法对其进行研究。通过构造新的增广Lyapunov-Krasovskii泛函,并对其导数采用一系列不等式方法进行界定,获得具有更小保守性的时滞相关指数同步判据。同时,基于最大采样间隔以及衰减率,得到可行控制器。最后,通过数值算例及仿真证明此方法的优越性以及可行性。
Sampled-data exponential synchronization problems for master-slave neural networks with time-varying mixed delays were investigated with the Lyapunov-Krasovskii functional approach and linear matrix inequality(LMI).By constructing the novel Lyapunov-Krasovskii functions and estimating the derivative of them with a set of inequality methods, exponential synchronization criteria with time-varying delays were derived, which had less conservative. Then, depending upon the maximum sampling interval and decay rate, the desired sampled-data controller was achieved. The numerical example and simulation results verify the superiority and effectiveness of the approach.
Sampled-data exponential synchronization problems for master-slave neural networks with time-varying mixed delays were investigated with the Lyapunov-Krasovskii functional approach and linear matrix inequality(LMI).By constructing the novel Lyapunov-Krasovskii functions and estimating the derivative of them with a set of inequality methods, exponential synchronization criteria with time-varying delays were derived, which had less conservative. Then, depending upon the maximum sampling interval and decay rate, the desired sampled-data controller was achieved. The numerical example and simulation results verify the superiority and effectiveness of the approach.
引文
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[15]ZHANG Chuanke,HE Yong,WU Min.Exponential synchronization of neural networks with time-varying mixed delays and sampled-data[J].Neurocomputing,2010,74(1/2/3):265-273.
[16]WU Zhengguang,SHI Peng,SU Yonghe,et al.Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling[J].IEEE Transactions on Neural Networks&Learning Systems,2012,23(9):1368-1376.
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[18]PARK P G,LEE W I,LEE S Y.Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems[J].Journal of the Franklin Institute,2015,352(4):1378-1396.
[19]KWON O M,JU H P,LEE S M.New augmented Lyapunov-Krasovskii functional approach to stability analysis of neural networks with time-varying delays[J].Nonlinear Dynamics,2014,76(1):221-236.
[2]BAI Yonggiang,CHEN Jie.New stability criteria for recurrent neural networks with interval time-varying delay[J].Neurocomputing,2013,121(18):179-184.
[3]GE Chao,HUA Changchun,GUAN Xinping.New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach[J].IEEE Transactions on Neural Networks and Learning Systems,2014,25(7):1378-1383.
[4]ZHANG Chuanke,HE Yong,JIANG Lin,et al.Delay-dependent stability criteria for generalized neural networks with two delay components[J].IEEE Transactions on Neural Networks&Learning Systems,2014,25(7):1263-1276.
[5]ZHANG Chuanke,HE Yong,JIANG Lin,et al.Delay-dependent stability analysis of neural networks with time-varying delay:a generalized free-weighting-matrix approach[J].Applied Mathematics&Computation,2017,294(C):102-120.
[6]ZENG Hongbing,HE Yong,WU Min,et al.Free-matrix-based integral inequality for stability analysis of systems with time-varying delay[J].IEEE Transactions on Automatic Control,2015,60(10):2768-2772.
[7]RAJA R,ZHU Quanxin,SENTHILRAJ S,et al.Improved stability analysis of uncertain neutral type neural networks with leakage delays and impulsive effects[J].Applied Mathematics&Computation,2015,266(C):1050-1069.
[8]ZENG Hongbing,HE Yong,WU Min,et al.Stability analysis of generalized neural networks with time-varying delays via a new integral inequality[J].Neurocomputing,2015,161(C):148-154.
[9]FATTAHI M,VASEGH N,MOMENI H R.Stabilization of a class of nonlinear discrete time systems with time varying delay[J].Journal of Central South University(Science and Technology),2014,21(10):3769-3776.
[10]WANG Xin,SHE Kun,ZHONG Shouming,et al.New result on synchronization of complex dynamical networks with time-varying coupling delay and sampled-data control[J].Neurocomputing,2016,214:508-515.
[11]WU Ming,LIU Fang,SHI Peng,et al.Exponential stability analysis for neural networks with time-varying delay[J].IEEE Transactions on Systems Man&Cybernetics Part B Cybernetics A Publication of the IEEE Systems Man&Cybernetics Society,2008,38(4):1152-1156.
[12]XIAO Shenping,ZHANG Xianming.New globally asymptotic stability criteria for delayed cellular neural networks[J].IEEE Transactions on Circuits&Systems II Express Briefs,2009,56(8):659-663.
[13]KWON O M,JU H P.New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays[J].Applied Mathematics&Computation,2008,205(1):417-427.
[14]YU Wenwu,CAO Jinde.Synchronization control of stochastic delayed neural networks[J].Physica A Statistical Mechanics&Its Applications,2007,373(1):252-260.
[15]ZHANG Chuanke,HE Yong,WU Min.Exponential synchronization of neural networks with time-varying mixed delays and sampled-data[J].Neurocomputing,2010,74(1/2/3):265-273.
[16]WU Zhengguang,SHI Peng,SU Yonghe,et al.Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling[J].IEEE Transactions on Neural Networks&Learning Systems,2012,23(9):1368-1376.
[17]RAKKIYAPPAN R,LATHA V P,ZHU Quanxin,et al.Exponential synchronization of Markovian jumping chaotic neural networks with sampled-data and saturating actuators[J].Nonlinear Analysis Hybrid Systems,2017,24:28-44.
[18]PARK P G,LEE W I,LEE S Y.Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems[J].Journal of the Franklin Institute,2015,352(4):1378-1396.
[19]KWON O M,JU H P,LEE S M.New augmented Lyapunov-Krasovskii functional approach to stability analysis of neural networks with time-varying delays[J].Nonlinear Dynamics,2014,76(1):221-236.