Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

Asymptotical Synchronization of Drive-Response Networks by Sample-Data-Based Event-Triggered Control with Quantization and Cyber-Attacks

Download PDF (1017.3 KB) PP. 55 - 73 Pub. Date: April 1, 2021

DOI: 10.22606/jaam.2021.62002


  • Ge Bai*
    College of Science, University of Shanghai for Science and Technology, Shanghai 200093, PR China


This paper addresses the asymptotic synchronization problem for a kind of drive-response complex networks (DRCNs) under cyber-attacks by using network control systems (NCSs). In order to reduce the pressure of communication and save the communication bandwidth on NCSs, some sampled-data-based event-triggered synchronization feedback controllers and logarithmic quantizers are designed by taking into account the effect of the NCSs’ transmission delays. Using Lyapunov stability theories, several sufficient conditions are obtained to guarantee the existence of sampleddata- based event-triggered synchronization controllers for the DRCNs with distributed-delay. Then, the state feedback gains are obtained by solving certain linear matrix inequalities (LMIs). Finally, a numerical example is provided to illustrate the effectiveness of the sampled-data-based eventtriggered control scheme.


synchronization control; event-triggered mechanism; sampled-data-based; network control system; quantization; cyber-attack


[1] S. H. Strogatz. Exploring complex networks. Nature, 410(8):268–276, 2001.

[2] R. Mikail and S. Olaf. Complex network measures of brain connectivity: uses and interpretations. Neuroimage, 52(3):1059–1069, 2010.

[3] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. U. Hwang. Complex networks: Structure and dynamics. phys.Rep., 424(4-5):175–308, 2006.

[4] B Shen, Z. D Wang, and X.H Liu. Sampled-data synchronization control of dynamical networks with stochastic sampling. IEEE Trans. Autom. Control, 57(10):2644–2650, 2012.

[5] X. Z Jin and G. H Yang. Adaptive synchronization of a class of uncertain complex networks against network deterioration. IEEE Trans. Circuits Sys.I, Reg. Papers, 58(6):1396–1409, 2011.

[6] Y Dong, J.WChen, and J. G Xian. Event-triggered control for finite-time lag synchronisation of time-delayed complex networks. IET Control Theory Appl., 12(14):1916–1923, 2018.

[7] H.S. Su, X.F Wang, and Z.L Lin. Synchronization of coupled harmonic oscillators in a dynamic proximity network. Automatica, 45(10):2286–2291, 2009.

[8] N. Mahdavi, M.B. Menhaj, J. Kurths, and J.Q. Lu. Fuzzy complex dynamical networks and its synchronization. IEEE Trans. Cybern, 43(2):648–659, 2013.

[9] G.Z. Feng and J.D. Cao. Master-slave synchronization of chaotic systems with a modified impulsive controller. Adv. Differ. Equ., 24:12 pages, 2013.

[10] J. Wu and X. Li. Finite-time adaptive synchronization of drive-rsponse two-layer networks. 2018 IEEE Conference on Decision and Control(CDC), 2019.

[11] G. Al-mahbashi, M.S. Md Noorani, Bakar S.A., and Al sawalha M.M. Robust projective lag synchronization indrive-response dynamical networks viaadaptive control. European Physical Journal Special Topics, 225(1):51–64, 2016.

[12] W.L. Guo, Francis Austin, S.H. Chen, and W. Sun. Pinning synchronization of the complex networks with non-delayed and delayed coupling. Phys. Lett. A, 373(17):1565–1572, 2009.

[13] M.L. Yang, Y.G. Liu, Z.S. You, and P. Sheng. Global synchronization for directed complex networks. Nonlinear Analysis: Real world Applications, 11:2127–2135, 2009.

[14] E. Fridman, U. Shaked, and U. Suplin. Input/output delay approach to robust sampled-data h∞ control. Syst.Control Lett, 54(3):271–282, 2005.

[15] Z. Wang, F. Yang, D. W. C. Ho, and X. Liu. Robust h∞ control for networked systems with random packet losses. IEEE Trans. Syst., Man, Cybern., B, Cybern., 37(4):916–924, 2007.

[16] D. Yue, Q.L. Han, and C. Peng. State feedback controller design of networked control systems. IEEE Trans. Circuits Syst. II: Exp. Briefs, 51(11):640–644, 2004.

[17] Y.G. Niu, T.G. Jia, X.Y. Wang, and F.W. Yang. Output-feedback control design for ncss subject to quantization anddropout. Inf. Sci., 179(21):3804–3813, 2009.

[18] H.R. Karimi. Robust h∞ filter design for uncertain linearsystems over network with network-induceddelays and output quantization. Model., Identificat. Control., 30(1):27–37, 2009.

[19] M. Yu, L.Wang, T.G. Chu, and G.M. Xie. Stabilization of networked control systems with data packetdropout and network delays via switching system approach. proc. 43rd IEEE conf. Decis. Control., pages 3539–3544, 2004.

[20] Y.F. Guo. Switched filtering for networked systems with multiple packet dropouts. Frankl. Inst., 354(7):3134– 3151, 2017.

[21] D. Yue, E.G. Tian, and Q.L. Han. A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans. Autom. Control, 58(2):475–481, 2013.

[22] Q. Li, B. Shen, J.L. Liang, and H.S. Shu. Event-triggered synchronization control for complex networks with uncertain inner coupling. Int. J. Genetal Syst., 44(2):212–225, 2015.

[23] P. Chen and Q.L. Han. On designing a novel self-triggered sampling scheme for networked control systems with data losses and communication delays. IEEE Trans. Ind. Electron., 63(2):1239–1248, 2016.

[24] L. Ding, Q.L. Han, and X.H. Ge. An overview of recent advances in event-triggered consensus of multiagent systems. IEEE Trans. Cybern., 48(4):1110–1123, 2018.

[25] B. Shen, Z.D. Wang, and H. Qiao. Event-triggered state estimation for discrete-time multidelayed neural networks with stochastic parameters and incomplete measurements. IEEE Trans. Neural Netw. Learn. Syst., 28(5):1152–1163, 2017.

[26] G. Guo, L. Ding, and Q.L. Han. A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems. Automatica, 50(5):1489–1496, 2014.

[27] C. Liu and F. Hao. Dynamic output-feedback control for linear systems by using event-triggered quantisation. IET Control Theory Appl., 9(8):1254–1263, 2015.

[28] J.K. Sun, J. Yang, S.H. Li, and W.X. Zheng. Sampled-data-based event-triggered active distrubance rejection control for distrubed systems in networked environment. IEEE Trans. Cybern., 49(2):556–566, 2019.

[29] S.L. Hu and D. Yue. Event-triggered control design of linear networked systems with quantizations. ISA Trans., 51(1):153–162, 2012.

[30] T.F. Liu and Z.P. Jiang. Event-triggered control design of nonlinear systems with quantization. IEEE Trans Autom Control., 64(2):797–803, 2019.

[31] B.C. Zheng, X.H. Yu, and Y.M. Xue. Quantized feedback sliding-mode control: An event-triggered approach. Automatic, 91:126–135, 2018.

[32] M.Y. Fu and L.H. Xie. The sector bound approach to quantized feedback control. IEEE Trans Autom Control., 50(11):1698–1711, 2005.

[33] H. Ishii and B.A. Francis. Quadratic stabilization of sampled-data systems with quantization. Automatic., 39(10):1793–1800, 2003.

[34] Y.C. Sun and G.H. Yang. Periodic event-triggered resilient control for cyber-physical systems under denialof- service attacks. J. Franklin. Inst., 335(13):5613–5631, 2018.

[35] H.T. Sun, C. Peng, W.D. Zhang, and T.C. Yang. Security-based resilient event-triggered control of networked control systems under denial of service attacks. J. Franklin. Inst., 356(17):10277–10295, 2018.

[36] C. Peng, J.C. Li, and M.R. Fei. Resilient event-triggering h∞ load frequency control for multi-area power systems with energy-limited dos attacks. IEEE Trans. Power Syst., 32(5):4110–4118, 2017.

[37] B. Chen, W.C. Ho, G.Q. Hu, and L. Yu. Secure fusion estimation for bandwidth constrained cyber-physical systems under replay attacks. IEEE Trans. Cybern., 48(6):1862–1876, 2018.

[38] Z.H. Pang and G.P. Liu. Design and implementation of secure networked predictive control systems under deception attacks. IEEE Trans. Control Syst. Technol., 20(5):1334–1342, 2012.

[39] W. Yang, L. Lei, and C. Yang. Event-based distributed state estimation under deception attack. Neurocomputing., 270:145–151, 2017.

[40] D.R. Ding, Z.D. Wang, W.C. Daniel, and G.L. Wei. Distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks. Automatic., 78:231–240, 2017.

[41] M.H. Zhu and S. Martinez. On the performance analysis of resilient networked control systems under replay attacks. IEEE Trans. Autom. Control, 59(3):804–808, 2014.

[42] J.L. Liu, L.L. Wei, E.G. Tian, S.M. Fei, and J. Cao. Hybrid-driven-based h∞ filtering design for networked systems under stochastic cyber attacks. Journal of the Franklin Institute, 354(18):8490–8512, 2017.

[43] H.J. Li. Sampled-data state estimation for complex dynamical networks with time-varying delay and stochastic sampling. Neurocomputing, 138(11):75–85, 2014.

[44] D. H. He and L.G. Xu. Boundedness analysis of stochastic integro-differential systems with lévy noise. J. Taibah 304Univ. Sci., (111):87–93, 2020.

[45] L. G. Xu and H. X. Hu. Boundedness analysis of stochastic pantograph differential systems. Appl. Math. Lett., 111(111):106630, 2021.