Abstract
The exponential sampling synchronization of complex network systems based on T–S fuzzy model is studied in this paper. Firstly, a modified Lyapunov–Krasovskii function (LKF) is designed. The linear matrix inequalities in the synchronization criterion are obtained by combining the efficient integral inequality and the free weighting matrix while processing the LKF differential results. Secondly, on the basis of Theorem 1, the full consideration of the interference caused by the time delay phenomenon in the actual production life, theorem 2 will fully solve this problem. The time delay is added during the sampling process, and the resulting synchronization criterion makes the system have better anti-interference performance than the original system. Finally, in the simulation part, two numerical simulations are proposed to verify the correctness and practical applicability of the obtained synchronization criterion.
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References
Chen Z, Shi KB, Zhong SM (2016) New synchronization criteria for complex delayed dynamical networks with sampled-data feedback control. ISA Trans 63:154–169
Ge C, Wang BF, Wei X et al (2017) Exponential synchronization of a class of neural networks with sampled-data control. Appl Math Comput 35:150–161
Guan ZH, Liu ZW, Feng G (2010) Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans Circ Syst Part I Regular Pap 57:2182–2195
Hellani DE, Hajjaji AE, Ceschi R (2018) Finite frequency \({{H}_{\infty }}\) filter design for T–S fuzzy systems: New approach. Signal Process 143:191–199
Hu C, Yu J, Jiang H, Teng Z (2011) Exponential synchronization of complex networks with finite distributed delays coupling. IEEE Trans Neural Netw 22:1999C2010
Huang XJ, Ma YC (2018) Finite-time \({H_\infty }\) sampled-data synchronization for Markovian jump complex networks with time-varying delays. Neurocomputing 296:82–99
Jun W, Yali D, Yongfeng S (2012) Exponential stabilization for uncertain T–S fuzzy systems with time-delay and nonlinear perturbation. IEEE Control Conf 31:1330–1335
Kaviarasan B, Sakthivel R, Lim Y (2016) Synchronization of complex dynamical networks with uncertain inner coupling and successive delays based on passivity theory. Neurocomputing 186:127–138
Li HJ (2014) Sampled-data state estimation for complex dynamical networks with time-varying delay and stochastic sampling. Neurocomputing 138:78–85
Li N, Zhang YL, Hu JW, Nie ZY (2011) Synchronization for general complex networks with sampled-data. Neurocomputing 74:805–811
Liu YJ, Lee SM (2015) Improved results on sampled-data synchronization of complex dynamical networks with time-varying coupling delay. Nonlinear Dyn 81:931–938
Ma YC, Chen MH (2015) Delay-dependent exponential \({{H}_{\infty }}\) filter for uncertain nonlinear singular time-delay systems through T–S fuzzy model. Adv Differ Equ 2015(1):245
Park MJ, Kwon OM, Park JH, Lee SM, Cha EJ (2015) Stability of time-delay systems via Wirtinger-based double integral inequality. Automatica 55:204–208
Qiu J, Feng G, Gao H (2011) Nonsynchronizated-state estimation of multichannel networked nonlinear systems with multiple packet dropouts via T–S fuzzy-affine dynamical models. IEEE Trans Fuzzy Syst 19:75–90
Sakthivel R, Karimi HR (2017) Resilient sampled-data control for Markovian jump systems with an adaptive fault-tolerant mechanism. IEEE Trans Circuits Syst II Express Briefs 64:1312–1316
Seuret A, Gouaisbaut F (2013) Wirtinger-based integral inequality: application to time-delay systems. Automatica 9:2860–2866
Shen B, Wang ZD, Liu XH (2012) Sampled-data synchronization control of dynamical networks with stochastic sampling. IEEE Trans Autom Control 57:2
Su H, Rong Z, Chen MZQ, Wang X, Chen G, Wang H (2013) Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks. IEEE Trans Syst Man Cybern B Cybern 43:394C399
Su L, Ye D, Yang X (2017) Dissipative-based sampled-data synchronization control for complex dynamical networks with time-varying delay. J Franklin Inst 354:6855–6876
Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132
Tanaka K, Sugeno M (1992) Stability analysis and design of fuzzy control systems. Fuzzy Sets Syst 45(2):135–156
Wang J, Zhang H, Wang Z, Wang B (2013) Local exponential synchronization in complex dynamical networks with time-varying delay and hybrid coupling. Appl Math Comput 225:16C32
Wang JY, Zhang HG, Wang ZS (2015) Sampled-data synchronization for complex networks based on discontinuous LKF and mixed convex combination. J Franklin Inst 352:4741–4757
Wang J, Zhang H, Wang Z, Liang H (2015) Stochastic synchronization for Markovian coupled neural networks with partial information on transition probabilities. Neurocomputing 149:983C992
Wang X, She K, Zhong SM et al (2016) New result on synchronization of complex dynamical networks with time-varying coupling delay and sampled-data control. Neurocomputing 214:508–515
Wang M, Qiu J, Chadli M et al (2017) A switched system approach to exponential stabilization of sampled-data T–S fuzzy systems with packet dropouts. IEEE Trans Cybern 46(12):3145–3156
Wang C, Cheng J, Barakati AA et al (2017) A mismatched membership function approach to sampled-data stabilization for T–S fuzzy systems with time-varying delayed signals. Signal Process 140:161–170
Watts D, Strogatz S (1998) Collective dynamical of small-world networks. Nature 393:440–442
Wong W, Zhang W, Tang Y, Wu X (2013) Stochastic synchronization of complex networks with mixed impulses. IEEE Trans Circuits Syst I Regul Pap 60:2657C2667
Wu HN, Li HX (2007) New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay. IEEE Trans Fuzzy Syst 15(3):482–493
Wu ZG, Shi P, Su H et al (2012) Reliable \({{H}_{\infty }}\) control for discrete-time fuzzy systems with infinite-distributed delay. IEEE Trans Fuzzy Syst 20(1):22–31
Wu ZG, Park JuH, Su HY et al (2012) Exponential synchronization for complex dynamical networks with sampled-data. J Franklin Inst 349:2735–2749
Wu YQ, Shi P, Su HY (2018) Sampled-data synchronization of complex networks with partial couplings and T–S fuzzy nodes. IEEE Trans Fuzzy Syst 26:782–793
Xie X, Xie J, Hu S (2015) Reducing the conservatism of stability conditions for continuous-time T–S fuzzy systems based on an extended approach. Neurocomputing 173:1655–1659
Xin X, Chen T, Cao J et al (2011) Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Netw 24:1013–1021
Yang X, Cao J, Lu J (2013) Synchronization of coupled neural networks with random coupling strengths and mixed probabilistic time-varyingdelays. Int J Robust Nonlinear Control 23:2060C2081
Yu W, Chen G, Lv J (2009) On pinning synchronization of complex dynamical networks. Automatica 45:429–435
Zhang CK, He Y, Wu M (2010) Exponential synchronization of neural networks with time-varying mixed delays and sampled-data. Neurocomputing 74:265–273
Zhang H, Zhao M, Wang Z, Wu Z (2014) Adaptive synchronization of an uncertain coupling complex network with time-delay. Nonlinear Dyn 77:643C653
Zhang H, Zhang J, Yang G (2015) Leader-based optimal coordination control for the consensus problem of multiagent differential games via fuzzy adaptive dynamic programming. IEEE Trans Fuzzy Syst 23:152–163
Zhao T, Dian S (2017) Fuzzy dynamic output feedback \({{H}_{\infty }}\) control for continuous-time T–S fuzzy systems under imperfect premise matching. ISA Trans 70:248–259
Zhao J, Hill DJ, Liu T (2009) Synchronization of complex dynamical networks with switching topology: aswitched system point of view. Automatica 45:2502C2511
Acknowledgements
This work is partially supported by the National Natural Science Foundation of China No. 61273004, and the Natural Science Foundation of Hebei province No. F2018203099.
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Communicated by Leonardo Tomazeli Duarte.
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Project supported by National Science Foundation of China (No. 61273004), and the Natural Science Foundation of Hebei province (No. F2018203099)
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Huang, X., Cao, X. & Ma, Y. Sampled-data exponential synchronization of complex dynamical networks with time-varying delays and T–S fuzzy nodes. Comp. Appl. Math. 41, 74 (2022). https://doi.org/10.1007/s40314-022-01778-6
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DOI: https://doi.org/10.1007/s40314-022-01778-6