The pinning synchronization problem is investigated for complex dynamical networks with hybrid coupling via impulsive control. Based on the Lyapunov stability theory, some novel synchronization criteria are derived and an impulsive pinning control law is proposed. By introducing a differential inequality for systems with piecewise constant arguments, it is not necessary to establish any relationship between the norms of the error states with or without piecewise constant arguments. Typical numerical examples are utilized to illustrate the validity and improvements as regards conservativeness of the theoretical results.
AkhmetMUYilmazE (2010) Impulsive Hopfield-type neural networks system with piecewise constant argument. Nonlinear Analysis – Real World Applications11: 2584–2593.
2.
AkhmetMUYilmazM (2012) Global exponential stability of neural networks with non-smooth and impact activations. Neural Networks34: 18–27.
3.
AlwanMSLiuXXieWC (2013) Comparison principle and stability of differential equations with piecewise constant arguments. Journal of the Franklin Institute350: 211–230.
4.
BagheriAOzgoliS (2016) Exponentially impulsive projective and lag synchronization between uncertain complex networks. Nonlinear Dynamics84: 2043–2055.
5.
BaoGWenSZengZ (2012) Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type. Neural Networks33: 32–41.
6.
CaiSHaoJHeQ. (2011) Exponential synchronization of complex delayed dynamical networks via pinning periodically intermittent control. Physics Letters A375: 1965–1971.
7.
CaiSLeiXLiuZ (2016) Outer synchronization between two hybrid-coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control. Complexity21: 593–605.
8.
ChandrasekarARakkiyappanR (2016) Impulsive controller design for exponential synchronization of delayed stochastic memristor-based recurrent neural networks. Neurocomputing173: 1348–1355.
9.
ChenWHJiangZYZhongJC. (2014) On designing decentralized impulsive controllers for synchronization of complex dynamical networks with nonidentical nodes and coupling delays. Journal of The Franklin Institute351: 4084–4110.
10.
CookeKLWienerJ (1984) Retarded differential equations with piecewise constant delays. Journal of Mathematical Analysis and Applications99: 265–297.
11.
DeLellisPdiBernardoGarofaloF (2013) Adaptive pinning control of networks of circuits and systems in Lur’e form. IEEE Transactions on Circuits and Systems I: Regular Papers60: 3033–3041.
12.
GuanZHLiuZWWangYW (2010) Synchronization of complex dynamical networks with time varying delays via impulsive distributed control. IEEE Transactions on Circuits and Systems I57: 2182–2194.
13.
HallET (1983) The Dance of Life: The Other Dimension of Time. New York, NY: Anchor Books.
14.
HeWQianFCaoJ (2017) Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control. Neural Networks85: 1–9.
15.
HeWQianFLamJ. (2015) Quasi-synchronization of heterogeneous dynamic networks via distributed impulsive control. Automatica62: 249–262.
16.
LiCYuWHuangT (2014) Impulsive synchronization scheme of stochastic complex networks with switching topology: Average time approach. Neural Networks54: 85–94.
17.
LiuBHillDJ (2008) Impulsive consensus for complex dynamical networks with nonidentical nodes and coupling time-delays. Siam Journal on Control and Optimization49: 315–338.
18.
LiuYYSlotineJJBarabasiAL (2011) Controllability of complex networks. Nature473: 167–173.
19.
LiuZHHuiPM (2007) Collective signaling behavior in a networked-oscillator model. Physica A383: 714–724.
20.
LuJKurthsJCaoJ. (2012) Synchronization control for nonlinear stochastic dynamical networks: Pinning impulsive strategy. IEEE Transactions on Neural Networks and Learning Systems23: 285–292.
21.
LuWChenT (2006) New approach to synchronization analysis of linear coupled ordinary differential systems. Physica D213: 214–230.
22.
MahdaviNMohammadMBKurthsJ. (2012) Pinning impulsive synchronization of complex dynamical networks. International Journal of Bifurcation and Chaos22: 1250239.
23.
MaXShaoYWangZ. (2016) An impulsive two-stage predator-prey model with stage-structure and square root functional responses. Mathematics and Computers in Simulation119: 91–107.
24.
ÖztükIBozkurtFGurcanF (2012) Stability analysis of a mathematical model in a microcosm with piecewise constant arguments. Mathematical Bioscience240: 85–91.
25.
PecoraLMCarrollTL (1990) Synchronization in chaotic systems. Physical Review Letters64: 821–824.
RivadeneiraPSMoogCH (2015) Observability criteria for impulsive control systems with applications to biomedical engineering processes. Automatica55: 125–131.
28.
ShahSMWienerJ (1983) Advanced differential equations with piecewise constant argument deviations. International Journal of Mathematics and Mathematical Sciences6: 671–703.
29.
ShenWZengZWenS (2016) Synchronization of complex dynamical network with piecewise constant argument of generalized type. Neurocomputing173: 671–675.
30.
SongQCaoJ (2010) On pinning synchronization of directed and undirected complex dynamical networks. IEEE Transactions on Circuits and Systems I: Regular Papers57: 672–680.
31.
SongQCaoJLiuF (2011) Synchronization of complex dynamical networks with nonidentical nodes. Physics Letters A374: 544–551.
WangFYangYHuM. (2015) Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control. Physica A434: 134–143.
34.
WattsDStrogatzS (1998) Collective dynamics of ‘small-world’ networks. Nature393: 440–442.
35.
WeiQXieCLiangY. (2016) Hybrid time-varying delay projective synchronization in complex dynamical networks. Transactions of the Institute of Measurement and Control3: 1–7.
36.
WuCWChuaLO (1995) Synchronization in an array of linearly coupled dynamical system. IEEE Transactions on Circuits and Systems I: Fundamental Theory Applications42: 430–447.
37.
WuWZhouWChenTP (2009) Cluster synchronization of linear coupled complex networks under pinning control. IEEE Transactions on Circuits and Systems I: Regular Papers56: 829–839.
38.
WuXTangYCaoJ. (2015) Distributed consensus of stochastic delayed multi-agent systems under asynchronous switching. IEEE Transactions on Cybernetics46: 1817–1827.
39.
WuZParkJHSuH. (2012) Exponential synchronization for complex dynamical networks with sampled-data. Journal of Franklin Institute349: 2735–2749.
40.
XiangZTangSXiangC (2015) On impulsive pest control using integrated intervention strategies. Applied Mathematics and Computation269: 930–946.
41.
YangXCaoJLuJ (2012) Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control. IEEE Transactions on Circuits and Systems I: Regular Papers59: 371–384.
42.
YangY (2012) Synchronization of complex dynamical networks under time delays with occurrence probabilities. Transactions of the Institute of Measurement and Control35: 437–443.
43.
YuTCaoD (2018) Stability analysis of impulsive neural networks with piecewise constant arguments. Neural Processing Letters. 47: 153–165.
44.
YuTCaoDLiuS. (2016a) Stability analysis of neural networks with periodic coefficients and piecewise constant arguments. Journal of the Franklin Institute353: 409–425.
45.
YuTCaoDYangY. (2016b) Robust synchronization of impulsively coupled complex dynamical network with delayed nonidentical nodes. Chaos, Solitons, and Fractals87: 92–101.
46.
YuWChenGLüJ (2009) On pinning synchronization of complex dynamical networks. Automatica45: 429–435.
47.
ZhangLWangYWangQ (2015) Synchronization for time-varying complex dynamical networks with different-dimensional nodes and non-dissipative coupling. Communication in Nonlinear Science and Numerical Simulation24: 64–74.
48.
ZhaoJHillDJLiuT (2011) Synchronization of dynamical networks with nonidentical nodes: Criteria and control. IEEE Transactions on Circuits and Systems I: Regular Papers58: 584–594.
49.
ZhaoJHillDJLiuT (2012) Global bounded synchronization of general dynamical networks with nonidentical nodes. IEEE Transactions on Automatic Control57: 2656–2662.
