Abstract
This paper addresses the problem of global exponential lag synchronization of switched neural networks with time-varying delays and general activation functions. Based on the Lyapunov–Krasovskii functional method and free weighting matrix technique, delay-dependent criteria for the global exponential lag synchronization of switched neural networks are derived in form of linear matrix inequalities. A numerical example is utilized to illustrate the characteristics of the results.


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Huang H, Qu Y, Li H (2005) Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty. Phys Lett A 345:345–354
Huang H, Feng G (2009) Synchronization of nonidentical chaotic neural networks with time delays. Neural Netw 22:869–874
He X, Li CD, Huang TW, Li CJ (2013) Codimension two bifurcation in a delayed neural network with unidirectional coupling. Nonlinear Anal RWA 14:1191–1202
He X, Li CD, Huang TW (2014) A Recurrent Neural Network for Solving Bilevel Linear Programming Problem. IEEE Trans Neural Netw Learn Syst 25(4):824–830
Yang X, Cao J, Liang J (2016) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst. doi:10.1109/TNNLS.2016.2561298
Guo Z, Wang J, Yan Z (2013) Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays. Neural Netw 48:158–172
Guo Z, Yang S, Wang J (2015) Global exponential synchronization of multiple memristive neural networks with time delay via nonlinear coupling. IEEE Trans Neural Netw Learn Syst 26(6):1300–1311
Guo Z, Wang J, Yan Z (2015) Global exponential synchronization of two memristor-based recurrent neural networks with time delays via static or dynamic coupling. IEEE Trans Syst Man Cybern Syst 45(2):235–249
Guo Z, Wang J, Yan Z (2014) Attractivity analysis of memristor-based cellular neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 25(4):704–717
Zhou L (2015) Delay-dependent exponential synchronization of recurrent neural networks with multiple proportional delays. Neural Process Lett 42(3):619–632
Wang X, Li C, Huang T, Duan S (2013) Global exponential stability of a class of memristive neural networks with time-varying delays. Neural Comput Appl. doi:10.1007/s00521-013-1383-1
Chen L, Li C, Huang T, Chen Y, Wang X (2013) Memristor crossbar-based unsupervised image learning. Neural Comput Appl. doi:10.1007/s00521-013-1501-0
Shen Y, Miao P, Huang Y et al (2015) Finite-time stability and its application for solving time-varying Sylvester equation by recurrent neural networks. Neural Process Lett 42(3):763–784
Li H, Liao X, Huang T, Wang Y, Han Q, Dong T (2014) Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies. Inform Sci 259:25–35
Zhou B, Liao X, Huang T, Wang H, Chen G (2015) Constrained consensus of asynchronous discrete-time multi-agent systems with time-varying topology. Inform Sci 320:223–234
Wang H, Liao X, Huang T, Chen G (2015) Distributed parameter estimation in unreliable WSNs: Quantized communication and asynchronous intermittent observation. Inform Sci 309:11–25
Yang X, Cao J, Qiu J (2015) \(p_{th}\) moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Netw 65:80–91
Chua L, Roska T (2002) Cellular networks and visual computing: foundations and applications. Cambridge University Press, Cambbridge
Chen G, Dong X (1998) From chaos to order: methodolgies, perspectives, and applications. World Scientific, Singapore
Zhang HG, Ma TD, Huang GB, Wang ZL (2010) Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control, IEEE Trans Syst Man Cybern B Cybern 40:831–844
Liang JL, Wang ZD, Liu YR, Li XH (2008) Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances. IEEE Trans Syst Man Cybern B Cybern 38:1073–1083
Wen S, Zeng Z, Huang T (2013) Passivity analysis of memristor-based recurrent neural networks with time-varying delays. J Frankl Inst 350:2354–2370
Cao JD, Chen GR, Li P (2008) Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Trans Syst Man Cybern B Cybern 38:488–498
Yang X, Cao J, Ho DWC (2015) Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control. Cognitive Neurodynam 9(2):113–128
Liu D, Wang D, Zhao D, Wei Q (2012) Neural-network-based optimal control for a class of unknown discrete-time nonlinear systems using globalized dual heuristic programming. IEEE Trans Autom Sci Eng 9:628–634
Yang X, Ho DWC (2015) Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Cybern. doi:10.1109/TCYB.2015.2505903
Liu Q, Dang C, Huang T (2013) A one-layer recurrent neural network for real-time portfolio optimization with probability criterion. IEEE Trans Cybern 43:14–23
Liu Q, Wang J (2013) A one-layer projection neural network for nonsmooth optimzation subject to linear equalities and bound constraints. IEEE Trans Neural Netw Learn Syst 24:812–824
Wen S, Zeng Z, Huang T, Meng Q, Yao W (2015) Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans Neural Netw Learn Syst 26(7):1493–1502
Wen G, Zhao Y, Duan Z, Yu W, Chen G. Containment of higher-order multi-leader multi-agent systems: a dynamic output approach. IEEE Trans Autom Control 61(4):1135–1140.
Wen S, Zeng Z, Chen M, Huang T (2016) Synchronization of switched neural networks with communication delays via the event-triggered control. IEEE Trans Neural Netw Learn Syst. doi:10.1109/TNNLS.2016.2580609
Wu A, Zeng Z (2012) Exponential stabilization of memristive neural networks with time delays. IEEE Trans Neural Netw Learn Syst 23:1919–1929
Wang L, Zhang R, Xu Z, Peng J (2009) Some characterizations of global exponential stability of a generic class of continuous-time recurrent neural networks. IEEE Trans Syst Man Cybern B Cybern 39:763–772
Zhang C, Zhang H, Wang Z (2011) Novel exponential stability criteria for high-order neural networks with time-varying delays. IEEE Trans Syst Man Cybern B Cybern 41:486–496
Wu L, Feng Z, Lam J (2013) Stability and synchronization of discrete-time neural networks wtih switching parameters and time-varying delays. IEEE Trans Neural Netw Learn Syst 24:1957–1972
Zeng H, He Y, Wu M, Zhang C (2011) Complete delay-decomposing approach to asymptotic stability for neural networks with time-arying delays. IEEE Trans Neural Netw 22:806–812
Huang T, Li C, Duan S, Starzyk J (2012) Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst 23:866–875
Li X, Gao H, Yu X (2011) A unified approach to the stability of generalized static neural networks wtih linear fractional uncertainties and delays. IEEE Trans Syst Man Cybern B Cybern 41:1275–1286
Yang X, Huang C, Cao J (2012) An LMI approach for exponential synchronization of switched stochastic competitive neural networks with mixed delays. Neural Comput Appl 21(8):2033–2047
Li C, Liao X (2007) Impulsive stabilization of delayed neural networks with and without uncertainty. Int J Robust Nonlinear Control 17(16):1489–1502
Wu E, Yang X (2015) Generalized lag synchronization of neural networks with discontinuous activations and bounded perturbations. Circuits Syst Signal Process 34(7):2381–2394
Song Q (2009) Design of controller on synchronization of chaotic neural networks with mixed time-varying delays. Neurocomputing 72(13–15):3288–3295
Rakkiyappan R, Chandrasekar A, Park JH, Kwon OM (2014) Exponential synchronization criteria for Markovian jumping neural networks with time-varying delays and sampled-data control. Nonlinear Anal Hybrid Syst 14:16–37
Chandrasekar A, Rakkiyappan R, Cao JD (2015) Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach. Neural Netw 70:27–38
Chandrasekar A, Rakkiyappan R (2016) Impulsive controller design for exponential synchronization of delayed stochastic Memristor-based recurrent neural networks. Neurocomputing 173:1348–1355
Chandrasekar A, Rakkiyappan R, Rihan FA, Lakshmanan S (2014) Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control. Neurocomputing 133:385–398
Rakkiyappan R, Dharani S, Zhu QX (2015) Stochastic sampled-data H-infinity Synchronization of coupled neutral-type delay partial differential systems. J Frankl Inst 352(10):4480–4502
Phat VN, Trinh H (2010) Exponential stabilization of neural networks with various activation functions and mixed time-varying delays. IEEE Trans Neural Netw 21:1180–1184
Liu Y, Wang Z, Liu X (2006) Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw 19(5):667–675
Wang Z, Shu H, Liu Y, Ho DWC, Liu X (2006) Robust stability analysis of generalized neural networks with discrete and distributed time delays. Chaos Solitons Fractals 30(4):886–896
Liu Y, Wang Z, Liu X (2006) On global exponential stability of generalized stochastic neural networks with mixed time delays. Neurocomputing 70(1–3):314–326
Zhao W, Tan Y (2007) Harmless delay for global exponential stability of Cohen–Grossberg neural networks. Math Comput Simul 74:47–57
Yue D, Tian E, Zhang Y, Peng C (2009) Delay-distribution-dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay. IEEE Trans Syst Man Cybern B Cybern 39:503–516
Peng C, Tian Y (2008) Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay. J Comput Appl Math 214:480–494
Xiong J, Lam J (2009) Stabilization of networked control systems with logic ZOH. IEEE Trans Automat Control 54:358–363
Gu K (2000) An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE conference decision control, Dec 2000, pp 2805–2810
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This work was supported by the Natural Science Foundation of China under Grants 61673187, 61403152, 61402218, and 61673188.
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Cao, Y., Wen, S. & Huang, T. New Criteria on Exponential Lag Synchronization of Switched Neural Networks with Time-Varying Delays. Neural Process Lett 46, 451–466 (2017). https://doi.org/10.1007/s11063-017-9599-1
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DOI: https://doi.org/10.1007/s11063-017-9599-1