The synchronization problem of coupled neural networks via impulsive control is investigated in the present paper. Based on a time varying Lyapunov functional associated with the impulsive time sequence, the delay-dependent criteria in terms of linear matrix inequalities are derived to guarantee the synchronization of the coupled neural networks. The obtained criteria are closely related to both the lower and the upper bound of the adjacent impulsive instant difference. By solving the corresponding linear matrix inequalities, the synchronization criteria can be used to estimate the upper bound of both transmission delay and distributed-delay. The low-dimensional criteria also are obtained for the coupled neural networks with identical nodes. Finally, two examples are given to illustrate the validity of the proposed hybrid control.
BagheriAOzgoliS (2016) Exponentially impulsive projective and lag synchronization between uncertain complex networks. Nonlinear Dynamics84(4): 2043–2055.
2.
CaoJChenGLiP(2008) Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics38(2): 488–498.
3.
ChenWHLuXZhengWX(2015) Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks. IEEE Transactions on Neural Networks and Learning Systems26(4): 734–748.
4.
ChenWHJiangZYZhongJC, et al (2014) On designing decentralized impulsive controllers for synchronization of complex dynamical networks with nonidentical nodes and coupling delays. Journal of the Franklin Institute351(8): 4084–4110.
5.
FeiZGuanCHaoH (2017) Exponential synchronization of networked chaotic delayed neural network by a hybrid event trigger scheme. IEEE Transactions on Neural Networks and Learning Systems99: 1–10.
6.
GuK (2000) An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE Conference on Decesion and Control. Syndey, 12–15 December, pp. 2805–2810, Australia: IEEE.
7.
HallET (1983) The Dance of Life: The Other Dimension of Time. New York: Anchor books.
8.
HePJingCFanT, et al (2014) Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties. Complexity19(3): 10–26.
9.
HeWQianFCaoJ (2017) Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control. Neural Networks85: 1–9.
10.
HeWZhangBHanQ, et al (2014) pinning synchronization of directed networks with aperiodic sampled-data communications. IEEE Transactions on Circuits and Systems I: Regular Papers61(11): 3245–3255.
11.
HuCJiangHTengZ (2010) Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms. IEEE Transactions on Neural Networks21(1): 67–81.
12.
HuJLiangJCaoJ (2014) Synchronization of hybrid-coupled heterogeneous networks: Pinning control and impulsive control schemes. Journal of The Franklin Institute351(5): 2600–2622.
13.
JiYLiuXDingF (2015) New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems. Nonlinear Dynamics79(1): 1–9.
14.
JiangPZengZChenJ (2015) Almost periodic solutions for a memristor-based neural networks with leakage, time-varying and distributed delays. Neural Networks68: 34–45.
15.
KhargonekarPPPetersenRIZhouK (1993) Robust stabilization of uncertain linear systems quadratic stabilizability and control theory. IEEE Transaction on Automatic Control35: 356–361.
16.
LengHWuZY (2016) Cluster synchronization of community network with distributed time delays via impulsive control. Chinese Physics B25(11): 159–166.
17.
LiNCaoJAlsaediA, et al (2017) Lag synchronization criteria for memristor-based coupled neural networks via parameter mismatches analysis approach. Neural Computation29(6): 1–24.
18.
LiXFangJLiH (2017) Master-slave exponential synchronization of delayed complex-valued memristor-based neural networks via impulsive control. Neural Networks93: 165–175.
19.
LiZFangJZhangW, et al (2015) Delayed impulsive synchronization of discrete-time complex networks with distributed delays. Nonlinear Dynamics82(4): 2081–2096.
20.
LiuYWangZLiuX (2006) Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Networks19(5): 667–675.
21.
LuJKurthsJCaoJ, et al. (2012) Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Transactions on Neural Networks and Learning Systems23(2): 285–292.
22.
LuWZhengRChenT (2016) Centralized and decentralized global outer-synchronization of asymmetric recurrent time-varying neural network by data-sampling. Neural Networks75: 22–31.
23.
MahdaviNMenhajMBKurthsJ (2012) Pinnig impulsive synchronization of complex dyanmical networks. International Journal of Bifurcation and Chaos22(10): 1250239.
24.
MacDonaldN (1980) Lecture Notes Biomath: Vol. 27. Time Lags in Biological Models. New York: Springer-Verlag.
25.
SenanSAli SyedMVadivelR, et al. (2017) Decentralized event-triggered synchronization of uncertain Markovian jumping neutral-type neural networks with mixed delays. Neural Networks86: 32–41.
26.
ShengYZengZ (2017) Synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and unbounded delays. Neural Networks93: 89–98.
27.
TangZParkJHFengJ (2017) Impulsive effects on quasi-synchronization of neural networks with parameter mismatches and time-varying delay. IEEE Transactions on Neural Networks and Learning Systems29(4): 908–919.
PengXWuHSongK, et al. (2017) Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays. Neural Networks94: 46–54.
30.
SuHRongZChenMZQ, et al. (2013) Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks. IEEE Transactions on Cybernetics43(1): 394–399.
31.
WeiPCWangJLHuangYL, et al. (2016) Impulsive control for the synchronization of coupled neural networks with reaction-diffusion terms. Neurocomputing207: 539–547.
32.
WenSZengZHuangT, et al. (2015) New criteria of passivity analysis for fuzzy time-delay systems with parameter uncertainties. IEEE Transactions on Fuzzy Systems23(6): 2284–2301.
33.
WuCWChuaLO (1995) Synchronization in an array of linearly coupled dynamical system. IEEE Transactions on Circuits Systems-I, Fundamential Theory and Applications42(8): 430–447.
34.
YangMWangYWXiaoJW, et al. (2010) Robust synchronization of impulsively-coupled complex switched networks with parametric uncertainties and time-varying delays. Nonlinear Analysis-Real World Applications11(4): 3008–3020.
35.
YangSLiCHuangT (2016) Exponential stabilization and synchronization for fuzzy model of memristive neural networks by periodically intermittent control. Neural Networks75: 162–172.
36.
YiCFengJWangJ, et al. (2017) Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control. Applied Mathematics and Computation312: 78–90.
37.
YuTCaoD (2018) Stability analysis of impulsive neural networks with piecewise constant arguments. Neural Processing Letters47(1): 153–165.
38.
YuTCaoDYangY, et al. (2016) Robust synchronization of impulsively coupled complex dynamical network with delayed nonidentical nodes. Chaos, Solitons, and Fractals26: 92–101.
39.
YuanK (2009) Robust synchronization in arrays of coupled networks with delay and mixed coupling. Neurocomputing72(4-6): 1026–1031.
40.
ZhangYSunJ (2009) Robust synchronization of coupled delayed neural networks under general impulsive control. Chaos, Solitons, and Fractals41(3): 1476–1480.
