Novel non-fragile extended dissipative synchronization of T-S fuzzy complex dynamical networks with interval hybrid coupling delays

Arthit Hongsri; Wajaree Weera; Thongchai Botmart; Prem Junsawang; Arthit Hongsri; Wajaree Weera; Thongchai Botmart; Prem Junsawang

doi:10.3934/math.20231464

AIMS Mathematics

2023, Volume 8, Issue 12: 28601-28627. doi: 10.3934/math.20231464

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Research article

Novel non-fragile extended dissipative synchronization of T-S fuzzy complex dynamical networks with interval hybrid coupling delays

1.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2.
Department of Statistics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 08 August 2023 Revised: 11 September 2023 Accepted: 17 September 2023 Published: 20 October 2023
MSC : 34D06, 05C82, 93B52

This paper presents the first investigation of extended dissipative synchronization in a specific type of Takagi-Sugeno (T-S) fuzzy complex dynamical networks with interval hybrid coupling delays. First, the decoupling method is employed to reorganize the multiple communication dynamical system, which comprises discrete-time, partial and distributed coupling delays. Second, the non-fragile control, which allows for uncertainty management within predefined norm bounds, has been applied to networks. Moreover, it becomes possible to derive a less conservative condition by utilizing multiple integral Lyapunov functionals, a decoupling strategy, Jensen's inequality, Wirtinger's inequality, and mathematical inequality techniques. This condition ensures that the T-S fuzzy complex dynamical networks, with interval hybrid coupling delays, can attain asymptotic synchronization with the assistance of a non-fragile feedback controller. Additionally, we extended this system to the extended dissipativity analysis, including passivity, $ L_2-L_\infty, H_{\infty} $ and dissipativity performance in a unified formulation. A set of strict linear matrix inequalities (LMIs) conditions is a sufficient criterion. Finally, two simulation examples are proposed to verify the merit of the obtained results.
- extended dissipative,
- synchronization,
- T-S fuzzy complex dynamical networks,
- hybrid coupling,
- delays,
- non-fragile control
Citation: Arthit Hongsri, Wajaree Weera, Thongchai Botmart, Prem Junsawang. Novel non-fragile extended dissipative synchronization of T-S fuzzy complex dynamical networks with interval hybrid coupling delays[J]. AIMS Mathematics, 2023, 8(12): 28601-28627. doi: 10.3934/math.20231464

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Abstract

This paper presents the first investigation of extended dissipative synchronization in a specific type of Takagi-Sugeno (T-S) fuzzy complex dynamical networks with interval hybrid coupling delays. First, the decoupling method is employed to reorganize the multiple communication dynamical system, which comprises discrete-time, partial and distributed coupling delays. Second, the non-fragile control, which allows for uncertainty management within predefined norm bounds, has been applied to networks. Moreover, it becomes possible to derive a less conservative condition by utilizing multiple integral Lyapunov functionals, a decoupling strategy, Jensen's inequality, Wirtinger's inequality, and mathematical inequality techniques. This condition ensures that the T-S fuzzy complex dynamical networks, with interval hybrid coupling delays, can attain asymptotic synchronization with the assistance of a non-fragile feedback controller. Additionally, we extended this system to the extended dissipativity analysis, including passivity, $ L_2-L_\infty, H_{\infty} $ and dissipativity performance in a unified formulation. A set of strict linear matrix inequalities (LMIs) conditions is a sufficient criterion. Finally, two simulation examples are proposed to verify the merit of the obtained results.

References

[1]	H. Jeong, B. Tombor, R. Albert, The large-scale organization of metabolic networks, Nature, 407 (2000), 651–654. http://dx.doi.org/10.1038/35036627 doi: 10.1038/35036627
[2]	S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), 268–276. http://dx.doi.org/10.1038/35065725 doi: 10.1038/35065725
[3]	R. J. Williams, E. L. Berlow, J. A. Dunne, A. L. Barabási, N. D. Martinez, Two degrees of separation in complex food webs, P. NatL. Acad. Sci. USA, 99 (2002), 12913–12916. http://dx.doi.org/10.1073/pnas.192448799 doi: 10.1073/pnas.192448799
[4]	A. Hongsri, T. Botmart, W. Weers, Improved on extended dissipative analysis for sampled-data synchronization of complex dynamical networks with coupling delays, IEEE Access, 10 (2022), 108625–108640. http://dx.doi.org/10.1109/ACCESS.2022.3213275 doi: 10.1109/ACCESS.2022.3213275
[5]	T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE T. Syst. Man. Cy.-S., 1 (1985), 116–132. http://dx.doi.org/10.1109/TSMC.1985.6313399 doi: 10.1109/TSMC.1985.6313399
[6]	Y. Wu, R. Lu, P. Shi, H. Su, Z. G. Wu, Sampled-data synchronization of complex networks with partial couplings and T-S fuzzy nodes, IEEE T. Fuzzy Syst., 2 (2017), 782–793. http://dx.doi.org/10.1109/TFUZZ.2017.2688490 doi: 10.1109/TFUZZ.2017.2688490
[7]	H. Divya, R. Sakthivel, Y. Liu, Delay-dependent synchronization of T-S fuzzy Markovian jump complex dynamical networks, Fuzzy Set. Syst., 416 (2021), 108–124. http://dx.doi.org/10.1016/j.fss.2020.10.010 doi: 10.1016/j.fss.2020.10.010
[8]	R. Sakthivel, R. Sakthivel, B. Kaviarasan, C. Wang, Y. K. Ma, Finite-time nonfragile synchronization of stochastic complex dynamical networks with semi-Markov switching outer coupling, Complexity, 2018 (2018), 1–13. http://dx.doi.org/10.1155/2018/8546304 doi: 10.1155/2018/8546304
[9]	Y. Han, S. Xiang, L. Zhang, Cluster synchronization in mutually-coupled semiconductor laser networks with different topologies, Opt. Commun., 445 (2019), 262–267. http://dx.doi.org/10.1016/j.optcom.2019.04.051 doi: 10.1016/j.optcom.2019.04.051
[10]	Y. Jin, S. Zhong, Function projective synchronization in complex networks with switching topology and stochastic effects, Appl. Math. Comput., 259 (2015), 730–740. http://dx.doi.org/10.1016/j.amc.2015.02.080 doi: 10.1016/j.amc.2015.02.080
[11]	X. Qiu, G. Zhu, Y. Ding, K. Li, Successive lag synchronization on complex dynamical networks via delay-dependent impulsive control, Physica A, 531 (2019), 1–15. http://dx.doi.org/10.1016/j.physa.2019.121753 doi: 10.1016/j.physa.2019.121753
[12]	X. Yang, Z. Yang, Synchronization of T-S fuzzy complex dynamical networks with time-varying impulsive delays and stochastic effects, Fuzzy Set. Syst., 235 (2014), 25–43. http://dx.doi.org/10.1016/j.fss.2013.06.008 doi: 10.1016/j.fss.2013.06.008
[13]	L. Zhao, H. Gao, H. R. Karimi, Robust stability and stabilization of uncertain T-S fuzzy systems with time-varying delay: An input-output approach, IEEE T. Fuzzy Syst., 21 (2013), 883–897. http://dx.doi.org/10.1109/TFUZZ.2012.2235840 doi: 10.1109/TFUZZ.2012.2235840
[14]	Y. Tang, J. A. Fang, M. Xia, X. Gu, Synchronization of Takagi-Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays, Appl. Math. Model., 34 (2010), 843–855. http://dx.doi.org/10.1109/TFUZZ.2010.2084570 doi: 10.1109/TFUZZ.2010.2084570
[15]	C. Zhou, L. Zemanová, G. Zamora, C. C. Hilgetag, J. Kurths, Hierarchical organization unveiled by functional connectivity in complex brain networks, Phys. Rev. Lett., 23 (2006), 1–4. http://dx.doi.org/10.1103/PhysRevLett.97.238103 doi: 10.1103/PhysRevLett.97.238103
[16]	X. Li, S. Song, Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays, IEEE T. Neur. Net. Lear., 24 (2013), 868–877. http://dx.doi.org/10.1109/TNNLS.2012.2236352 doi: 10.1109/TNNLS.2012.2236352
[17]	X. Li, J. Cao, An impulsive delay inequality involving unbounded time-varying delay and applications, IEEE T. Automat. Contr., 62 (2017), 3618–3625. http://dx.doi.org/10.1109/TAC.2017.2669580 doi: 10.1109/TAC.2017.2669580
[18]	C. Huang, D. W. Ho, J. Lu, J. Kurths, Pinning synchronization in T-S fuzzy complex networks with partial and discrete-time couplings, IEEE T. Fuzzy Syst., 23 (2014), 1274–1285. http://dx.doi.org/10.1109/TFUZZ.2014.2350534 doi: 10.1109/TFUZZ.2014.2350534
[19]	W. He, F. Qian, J. Cao, Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control, Neural Networks, 85 (2017), 1–9. http://dx.doi.org/10.1016/j.neunet.2016.09.002 doi: 10.1016/j.neunet.2016.09.002
[20]	Z. Wang, Y. Liu, K. Fraser, X. Liu, Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays, Phys. Lett. A, 354 (2006), 288–297. http://dx.doi.org/10.1016/j.physleta.2006.01.061 doi: 10.1016/j.physleta.2006.01.061
[21]	G. Rajchakit, R. Sriraman, R. Lim, C. P. Sam-ang, P. Hammachukiattikul, Synchronization in finite-time analysis of Clifford-valued neural networks with finite-time distributed delays, Mathematics, 9 (2021), 1–18. http://dx.doi.org/10.3390/math9111163 doi: 10.3390/math9111163
[22]	G. Ling, X. Liu, M. F. Ge, Y. Wu, Delay-dependent cluster synchronization of time-varying complex dynamical networks with noise via delayed pinning impulsive control, J. Franklin I., 358 (2021), 3193–3214. http://dx.doi.org/10.1016/j.jfranklin.2021.02.004 doi: 10.1016/j.jfranklin.2021.02.004
[23]	Z. Xu, P. Shi, H. Su, Z. G. Wu, T. Huang, Global $ H_\infty $ pinning synchronization of complex networks with sampled-data communications, IEEE T. Neur. Net. Lear., 29 (2017), 1467–1476. http://dx.doi.org/10.1109/TNNLS.2017.2673960 doi: 10.1109/TNNLS.2017.2673960
[24]	T. Jing, D. Zhang, J. Mei, Y. Fan, Finite-time synchronization of delayed complex dynamic networks via aperiodically intermittent control, J. Franklin I., 356 (2019), 5464–5484. http://dx.doi.org/10.1016/j.jfranklin.2019.03.024 doi: 10.1016/j.jfranklin.2019.03.024
[25]	J. A. Wang, Synchronization of delayed complex dynamical network with hybrid-coupling via aperiodically intermittent pinning control, J. Franklin I., 354 (2017), 1833–1855. http://dx.doi.org/10.1016/j.jfranklin.2016.11.034 doi: 10.1016/j.jfranklin.2016.11.034
[26]	Z. Qin, J. L. Wang, Y. L. Huang, S. Y. Ren, Analysis and adaptive control for robust synchronization and $H_\infty$ synchronization of complex dynamical networks with multiple time-delays, Neurocomputing, 289 (2018), 241–251. http://dx.doi.org/10.1016/j.neucom.2018.02.031 doi: 10.1016/j.neucom.2018.02.031
[27]	P. Delellis, M. D. Bernardo, F. Garofalo, Novel decentralized adaptive strategies for the synchronization of complex networks, Automatica, 45 (2009), 1312–1318. http://dx.doi.org/10.1016/j.automatica.2009.01.001 doi: 10.1016/j.automatica.2009.01.001
[28]	Y. Zhong, D. Song, Nonfragile synchronization control of T-S fuzzy Markovian jump complex dynamical networks, Chaos Soliton. Fract., 170 (2023), 1–9. http://dx.doi.org/10.1016/j.chaos.2023.113342 doi: 10.1016/j.chaos.2023.113342
[29]	Q. Dong, S. Shi, Y. Ma, Non-fragile synchronization of complex dynamical networks with hybrid delays and stochastic disturbance via sampled-data control, ISA T., 105 (2020), 174–189. http://dx.doi.org/10.1016/j.isatra.2020.05.047 doi: 10.1016/j.isatra.2020.05.047
[30]	D. Li, Z. Wang, G. Ma, Controlled synchronization for complex dynamical networks with random delayed information exchanges: A non-fragile approach, Neurocomputing, 171 (2016), 1047–1052. http://dx.doi.org/10.1016/j.neucom.2015.07.041 doi: 10.1016/j.neucom.2015.07.041
[31]	E. Gyurkovics, K. Kiss, A. Kazemy, Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control, J. Franklin I., 355 (2018), 8934–8956. http://dx.doi.org/10.1016/j.jfranklin.2018.10.005 doi: 10.1016/j.jfranklin.2018.10.005
[32]	R. Rakkiyappan, R. Sasirekha, S. Lakshmanan, C. P. Lim, Synchronization of discrete-time Markovian jump complex dynamical networks with random delays via non-fragile control, J. Franklin I., 353 (2016), 4300–4329. http://dx.doi.org/10.1016/j.jfranklin.2016.07.024 doi: 10.1016/j.jfranklin.2016.07.024
[33]	M. J. Park, O. M. Kwon, J. H. Park, S. M. Lee, E. J. Chae, Synchronization of discrete-time complex dynamical networks with interval time-varying delays via non-fragile controller with randomly occurring perturbation, J. Franklin I., 351 (2014), 4850–4871. http://dx.doi.org/10.1016/j.jfranklin.2014.07.020 doi: 10.1016/j.jfranklin.2014.07.020
[34]	G. Fan, Y. Ma, Non-fragile delay-dependent pinning $H_\infty$ synchronization of T-S fuzzy complex networks with hybrid coupling delays, Inf. Sci., 608 (2022), 1317–1333. http://dx.doi.org/10.1016/j.ins.2022.07.045 doi: 10.1016/j.ins.2022.07.045
[35]	R. Manivannan, J. Cao, K. T. Chong, Generalized dissipativity state estimation for genetic regulatory networks with interval time-delay signals and leakage delays, Commun. Nonlinear Sci., 89 (2020), 1–22. http://dx.doi.org/10.1016/j.cnsns.2020.105326 doi: 10.1016/j.cnsns.2020.105326
[36]	R. Saravanakumar, G. Rajchakit, M. S. Ali, Z. Xiang, Y. H. Joo, Robust extended dissipativity criteria for discrete-time uncertain neural networks with time-varying delays, Neural Comput. Appl., 30 (2018), 3893–3904. http://dx.doi.org/10.1007/s00521-017-2974-z doi: 10.1007/s00521-017-2974-z
[37]	B. Zhang, W. X. Zheng, S. Xu, Filtering of Markovian jump delay systems based on a new performance index, IEEE T. Circuits-I, 60 (2013), 1250–1263. http://dx.doi.org/10.1109/TCSI.2013.2246213 doi: 10.1109/TCSI.2013.2246213
[38]	Z. Feng, W. X. Zhang, On extended dissipativity of discrete-time neural networks with time delay, IEEE T. Neur. Net. Lear., 26 (2015), 3293–3300. http://dx.doi.org/10.1109/TNNLS.2015.2399421 doi: 10.1109/TNNLS.2015.2399421
[39]	H. Yang, L. Shu, S. Zhong, X. Wang, Extended dissipative exponential synchronization of complex dynamical systems with coupling delay and sampled-data control, J. Franklin I., 26 (2016), 1829–1847. http://dx.doi.org/10.1016/j.jfranklin.2016.03.003 doi: 10.1016/j.jfranklin.2016.03.003
[40]	Y. A. Liu, J. Xia, B. Meng, X. Song, H. Shen, Extended dissipative synchronization for semi-Markov jump complex dynamic networks via memory sampled-data control scheme, J. Franklin I., 357 (2020), 10900–10920. http://dx.doi.org/10.1016/j.jfranklin.2020.08.023 doi: 10.1016/j.jfranklin.2020.08.023
[41]	Y. Zhang, S. Liu, R. Yang, Global synchronization of fractional coupled networks with discrete and distributed delays, Physica A, 514 (2019), 830–837. http://dx.doi.org/https://doi.org/10.1016/j.physa.2018.09.129 doi: 10.1016/j.physa.2018.09.129
[42]	X. Wang, J. H. Park, H. Yang, X. Zhang, S. Zhong, Delay-dependent fuzzy sampled-data synchronization of T-S fuzzy complex networks with multiple couplings, IEEE T. Fuzzy Syst., 28 (2019), 178–189. http://dx.doi.org/10.1109/TFUZZ.2019.2901353 doi: 10.1109/TFUZZ.2019.2901353
[43]	O. M. Kwon, M. J. Park, J. H. Park, S. M. Lee, E. J. Cha, Analysis on robust $H_\infty$ performance and stability for linear systems with interval time-varying state delays via some new augmented Lyapunov-Krasovskii functional, Appl. Math. Comput., 224 (2013), 108–122. http://dx.doi.org/10.1016/j.amc.2013.08.068 doi: 10.1016/j.amc.2013.08.068
[44]	C. Peng, Y. C. Tian, Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay, J. Comput. Appl. Math., 214 (2008), 480–494. http://dx.doi.org/10.1016/j.cam.2007.03.009 doi: 10.1016/j.cam.2007.03.009

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