Improved results on sampled-data synchronization control for chaotic Lur'e systems

Xinyu Li; Wei Wang; Jinming Liang; Xinyu Li; Wei Wang; Jinming Liang

doi:10.3934/math.2025337

AIMS Mathematics

2025, Volume 10, Issue 3: 7355-7369. doi: 10.3934/math.2025337

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Improved results on sampled-data synchronization control for chaotic Lur'e systems

School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China

Received: 16 January 2025 Revised: 26 February 2025 Accepted: 13 March 2025 Published: 31 March 2025
MSC : 34D20

This paper examines the problem of master-slave synchronization control for chaotic Lur'e systems (CLS) under sampled-data conditions. Initially, a two-sided looped Lyapunov function is constructed by fully leveraging the system characteristics and information regarding the sampling mode. Subsequently, based on the Lyapunov stability theory and using the integral inequality of free matrices, we establish the stability criteria for the synchronization error system of CLS. Utilizing these conditions, we compute the sampling controller gains through an enhanced iterative conditioned cone complementarity linearization iteration algorithm, thereby achieving synchronization of the master-slave system over more extended sampling periods. Ultimately, numerical examples are presented to demonstrate that the proposed method outperforms existing approaches documented in the literature.
- Lur'e systems,
- synchronization,
- cone complementary linearization algorithm,
- sampled-data control
Citation: Xinyu Li, Wei Wang, Jinming Liang. Improved results on sampled-data synchronization control for chaotic Lur'e systems[J]. AIMS Mathematics, 2025, 10(3): 7355-7369. doi: 10.3934/math.2025337

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Abstract

This paper examines the problem of master-slave synchronization control for chaotic Lur'e systems (CLS) under sampled-data conditions. Initially, a two-sided looped Lyapunov function is constructed by fully leveraging the system characteristics and information regarding the sampling mode. Subsequently, based on the Lyapunov stability theory and using the integral inequality of free matrices, we establish the stability criteria for the synchronization error system of CLS. Utilizing these conditions, we compute the sampling controller gains through an enhanced iterative conditioned cone complementarity linearization iteration algorithm, thereby achieving synchronization of the master-slave system over more extended sampling periods. Ultimately, numerical examples are presented to demonstrate that the proposed method outperforms existing approaches documented in the literature.

References

[1]	A. T. Azar, F. E. Serrano, Q. Zhu, M. Bettayeb, G. Fusco, J. Na, et al., Robust stabilization and synchronization of a novel chaotic system with input saturation constraints, Entropy, 23 (2021), 1110. https://doi.org/10.3390/e23091110 doi: 10.3390/e23091110
[2]	J. Wang, K. Shi, Q. Huang, S. Zhong, D. Zhang, Stochastic switched sampled-data control for synchronization of delayed chaotic neural networks with packet dropout, Appl. Math. Comput., 335 (2018), 211–230. https://doi.org/10.1016/j.amc.2018.04.038 doi: 10.1016/j.amc.2018.04.038
[3]	K. Shi, Y. Tang, X. Liu, S. Zhong, Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation, ISA T., 66 (2017), 185–199. https://doi.org/10.1016/j.isatra.2016.11.002 doi: 10.1016/j.isatra.2016.11.002
[4]	T. H. Lee, J. H. Park, S. M. Lee, O. M. Kwon, Robust synchronization of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control, Int. J. Control, 86 (2013), 107–119. https://doi.org/10.1080/00207179.2012.720034 doi: 10.1080/00207179.2012.720034
[5]	B. Kaviarasan, R. Kavikumar, O. M. Kwon, R. Sakthivel, A delay-product-type lyapunov functional approach for enhanced synchronization of chaotic Lur'e systems using a quantized controller, AIMS Math., 9 (2024), 13843–13860. https://doi.org/10.3934/math.2024673 doi: 10.3934/math.2024673
[6]	J. G. Lu, D. J. Hill, Global asymptotical synchronization of chaotic Lur'e systems using sampled data: A linear matrix inequality approach, IEEE T. Circuits II, 55 (2008), 586–590. https://doi.org/10.1109/TCSII.2007.916788 doi: 10.1109/TCSII.2007.916788
[7]	Y. Kim, Y. Lee, S. Lee, P. Selvaraj, R. Sakthivel, O. Kwon, Design and experimentation of sampled-data controller in T-S fuzzy systems with input saturation through the use of linear switching methods, AIMS Math., 9 (2024), 2389–2410. https://doi.org/10.3934/math.2024118 doi: 10.3934/math.2024118
[8]	T. Yu, J. Cao, K. Lu, Finite-time synchronization control of networked chaotic complex-valued systems with adaptive coupling, IEEE T. Netw. Sci. Eng., 9 (2022), 2510–2520. https://doi.org/10.1109/TNSE.2022.3164773 doi: 10.1109/TNSE.2022.3164773
[9]	L. Zhao, G. H. Yang, Adaptive sliding mode fault tolerant control for nonlinearly chaotic systems against dos attack and network faults, J. Franklin I., 354 (2017), 6520–6535. https://doi.org/10.1016/j.jfranklin.2017.08.005 doi: 10.1016/j.jfranklin.2017.08.005
[10]	W. Jiang, H. Wang, J. Lu, G. Cai, W. Qin, Synchronization for chaotic systems via mixed-objective dynamic output feedback robust model predictive control, J. Franklin I., 354 (2017), 4838–4860. https://doi.org/10.1016/j.jfranklin.2017.05.007 doi: 10.1016/j.jfranklin.2017.05.007
[11]	W. Ji, Y. Jiang, J. Sun, Y. Zhu, S. Wang, On stability and ${H}_{\infty}$ control synthesis of sampled-data systems: A multiple convex function approximation approachl, Int. J. Robust Nonlin., 34 (2024), 7655–7678. https://doi.org/10.1002/rnc.7359 doi: 10.1002/rnc.7359
[12]	D. Tong, B. Ma, Q. Chen, Y. Wei, P. Shi, Finite-time synchronization and energy consumption prediction for multilayer fractional-order networks, IEEE T. Circuits II, 70 (2023), 2176–2180. https://doi.org/10.1109/TCSII.2022.3233420 doi: 10.1109/TCSII.2022.3233420
[13]	S. Zhu, J. Lu, S. i. Azuma, W. X. Zheng, Strong structural controllability of boolean networks: Polynomial-time criteria, minimal node control, and distributed pinning strategies, IEEE T. Automat. Contr., 68 (2023), 5461–5476. https://doi.org/10.1109/TAC.2022.3226701 doi: 10.1109/TAC.2022.3226701
[14]	D. Zeng, R. Zhang, Y. Liu, S. Zhong, Sampled-data synchronization of chaotic Lur'e systems via input-delay-dependent-free-matrix zero equality approach, Appl. Math. Comput., 315 (2017), 34–46. https://doi.org/10.1016/j.amc.2017.07.039 doi: 10.1016/j.amc.2017.07.039
[15]	Q. Zhu, Event-triggered sampling problem for exponential stability of stochastic nonlinear delay systems driven by lévy processes, IEEE T. Automat. Contr., 70 (2025), 1176–1183. https://doi.org/10.1109/TAC.2024.3448128 doi: 10.1109/TAC.2024.3448128
[16]	W. Wang, R. K. Xie, L. Ding, Stability analysis of load frequency control systems with electric vehicle considering time-varying delay, IEEE Access, 13 (2025), 3562–3571. https://doi.org/10.1109/ACCESS.2024.3519343 doi: 10.1109/ACCESS.2024.3519343
[17]	H. B. Zeng, K. L. Teo, Y. He, A new looped-functional for stability analysis of sampled-data systems, Automatica, 82 (2017), 328–331. https://doi.org/10.1016/j.automatica.2017.04.051 doi: 10.1016/j.automatica.2017.04.051
[18]	X. Yang, Q. Zhu, H. Wang, Exponential stabilization of stochastic systems via novel event-triggered switching controls, IEEE T. Automat. Contr., 69 (2024), 7948–7955. https://doi.org/10.1109/TAC.2024.3406668 doi: 10.1109/TAC.2024.3406668
[19]	H. B. Zeng, Y. J. Chen, Y. He, X. M. Zhang, A delay-derivative-dependent switched system model method for stability analysis of linear systems with time-varying delay, Automatica, 175 (2025), 112183. https://doi.org/10.1016/j.automatica.2025.112183 doi: 10.1016/j.automatica.2025.112183
[20]	H. B. Zeng, Z. L. Zhai, H. Yan, W. Wang, A new looped functional to synchronize neural networks with sampled-data control, IEEE T. Neur. Net. Lear., 33 (2022), 406–415. https://doi.org/10.1109/TNNLS.2020.3027862 doi: 10.1109/TNNLS.2020.3027862
[21]	Y. Liu, L. Tong, J. Lou, J. Lu, J. Cao, Sampled-data control for the synchronization of boolean control networks, IEEE T. Cybernetics, 49 (2019), 726–732. https://doi.org/10.1109/TCYB.2017.2779781 doi: 10.1109/TCYB.2017.2779781
[22]	W. H. Chen, Z. Wang, X. Lu, On sampled-data control for master-slave synchronization of chaotic Lur'e systems, IEEE T. Circuits II, 59 (2012), 515–519. https://doi.org/10.1109/TCSII.2012.2204114 doi: 10.1109/TCSII.2012.2204114
[23]	C. K. Zhang, L. Jiang, Y. He, Q. Wu, M. Wu, Asymptotical synchronization for chaotic Lur'e systems using sampled-data control, Commun. Nonlinear Sci., 18 (2013), 2743–2751. https://doi.org/10.1016/j.cnsns.2013.03.008 doi: 10.1016/j.cnsns.2013.03.008
[24]	C. Ge, C. Hua, X. Guan, Master-slave synchronization criteria of Lur'e systems with time-delay feedback control, Appl. Math. Comput., 244 (2014), 895–902. https://doi.org/10.1016/j.amc.2014.07.045 doi: 10.1016/j.amc.2014.07.045
[25]	K. Shi, X. Liu, H. Zhu, S. Zhong, Y. Zeng, C. Yin, Novel delay-dependent master-slave synchronization criteria of chaotic Lur'e systems with time-varying-delay feedback control, Appl. Math. Comput., 282 (2016), 137–154. https://doi.org/10.1016/j.amc.2016.01.062 doi: 10.1016/j.amc.2016.01.062
[26]	T. H. Lee, J. H. Park, Improved criteria for sampled-data synchronization of chaotic Lur'e systems using two new approaches, Nonlinear Anal. Hybri., 24 (2017), 132–145. https://doi.org/10.1016/j.nahs.2016.11.006 doi: 10.1016/j.nahs.2016.11.006
[27]	L. Yao, Z. Wang, X. Huang, Y. Li, Q. Ma, H. Shen, Stochastic sampled-data exponential synchronization of Markovian jump neural networks with time-varying delays, IEEE T. Neur. Net. Lear., 34 (2023), 909–920. https://doi.org/10.1109/TNNLS.2021.3103958 doi: 10.1109/TNNLS.2021.3103958
[28]	E. Fridman, A refined input delay approach to sampled-data control, Automatica, 46 (2010), 421–427. https://doi.org/10.1016/j.automatica.2009.11.017 doi: 10.1016/j.automatica.2009.11.017
[29]	W. Zhang, Q. L. Han, Y. Tang, Y. Liu, Sampled-data control for a class of linear time-varying systems, Automatica, 103 (2019), 126–134. https://doi.org/10.1016/j.automatica.2019.01.027 doi: 10.1016/j.automatica.2019.01.027
[30]	W. Liu, J. Huang, Output regulation of linear systems via sampled-data control, Automatica, 113 (2020), 108684. https://doi.org/10.1016/j.automatica.2019.108684 doi: 10.1016/j.automatica.2019.108684
[31]	C. K. Zhang, Y. He, M. Wu, Improved global asymptotical synchronization of chaotic Lur'e systems with sampled-data control, IEEE T. Circuits. II, 56 (2009), 320–324. https://doi.org/10.1109/TCSII.2009.2015388 doi: 10.1109/TCSII.2009.2015388
[32]	R. Zhang, D. Zeng, S. Zhong, Novel master-lave synchronization criteria of chaotic Lur'e systems with time delays using sampled-data control, J. Franklin I., 354 (2017), 4930–4954. https://doi.org/10.1016/j.jfranklin.2017.05.008 doi: 10.1016/j.jfranklin.2017.05.008
[33]	H. B. Zeng, W. M. Wang, W. Wang, H. Q. Xiao, Improved looped-functional approach for dwell-time-dependent stability analysis of impulsive systems, Nonlinear Anal. Hybri., 52 (2024), 101477. https://doi.org/10.1016/j.nahs.2024.101477 doi: 10.1016/j.nahs.2024.101477
[34]	Z. Zhai, H. Yan, S. Chen, H. Zeng, D. Zhang, Improved fragmentation looped-functional for synchronization of chaotic Lur'e systems, IEEE T. Circuits II, 69 (2022), 3550–3554. https://doi.org/10.1109/TCSII.2022.3167248 doi: 10.1109/TCSII.2022.3167248
[35]	H. B. Zeng, Z. J. Zhu, T. S. Peng, W. Wang, X. M. Zhang, Robust tracking control design for a class of nonlinear networked control systems considering bounded package dropouts and external disturbance, IEEE T. Fuzzy Syst., 32 (2024), 3608–3617. https://doi.org/10.1109/TFUZZ.2024.3377799 doi: 10.1109/TFUZZ.2024.3377799
[36]	Y. He, G. P. Liu, D Ress, M. Wu, Improved stabilisation method for networked control systems, IET Control Theory A., 1 (2007), 1580–1585. https://doi.org/10.1049/iet-cta:2007001 doi: 10.1049/iet-cta:2007001
[37]	W. M. Wang, H. B. Zeng, J. M. Liang, S. P. Xiao, Sampled-data-based load frequency control for power systems considering time delays, J. Franklin I., 362 (2025), 107477. https://doi.org/10.1016/j.jfranklin.2024.107477 doi: 10.1016/j.jfranklin.2024.107477
[38]	H. B. Zeng, Y. He, M. Wu, J. She, Free-matrix-based integral inequality for stability analysis of systems with time-varying delay, IEEE T. Automat. Contr., 60 (2015), 2768–2772. https://doi.org/10.1109/TAC.2015.2404271 doi: 10.1109/TAC.2015.2404271

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