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Synchronization Stability Criteria for Lur’e Systems via Delay-Product-Type Functional Method

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Abstract

This paper investigates the \({{\varvec{H}}}_{\infty }\) synchronization problem of chaotic Lur’e systems (CLs) with disturbance and uncertainties. First, for the bandwidth-constrained communication channel, a sampled-data controller is introduced to ensure that the master–slave CLs is synchronous. Then, according to the input delay approach, the dynamics of the considered synchronization error system is modeled by a delay system with disturbance and uncertainties. The main purpose of the problem addressed is to design a sampled-data controller, such that the synchronization error system guarantees the asymptotic stability with \({{\varvec{H}}}_{\infty }\) performance index. In order to obtain less conservative stability conditions, a delay-product-type Lyapunov–Krasovskii functional based on the N-order canonical Bessel–Legendre inequality is constructed. Furthermore, the sufficient conditions of stability with \({{\varvec{H}}}_{\infty }\) control performance are given as the basis of controller design. Finally, two illustrative examples are given to demonstrate the advantages of the proposed controller design scheme.

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References

  1. C. Ge, C. Hua, X. Guan, Master-slave synchronization criteria of Lur’e systems with time-delay feedback control. Appl. Math. Comput. 244, 895–902 (2014)

    MathSciNet  MATH  Google Scholar 

  2. C. Ge, J.H. Park, C. Hua, C. Shi, Robust passivity analysis for uncertain neural networks with discrete and distributed time-varying delays. Neurocomputing 364, 330–337 (2019)

    Article  Google Scholar 

  3. C. Ge, Y. Shi, J.H. Park, C. Hua, Robust \(H_{\infty }\) stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control. Appl. Math. Comput. 346, 500–512 (2019)

    MathSciNet  MATH  Google Scholar 

  4. C. Ge, B. Wang, X. Wei, Y. Liu, Exponential synchronization of a class of neural networks with sampled-data control. Appl. Math. Comput. 315, 150–161 (2017)

    MathSciNet  MATH  Google Scholar 

  5. Q. Hai, Further results on sampled-data synchronization control for chaotic Lur’e systems with time delay. Circuits, Syst. Signal Process. 41(1), 2–27 (2022)

    Article  Google Scholar 

  6. C. Hua, S.X. Ding, X. Guan, Robust controller design for uncertain multiple-delay systems with unknown actuator parameters. Automatica 48(1), 211–218 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. C. Hua, K. Li, X. Guan, Semi-global/global output consensus for nonlinear multiagent systems with time delays. Automatica 103, 480–489 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  8. C. Hua, S. Wu, X. Guan, Stabilization of T-S fuzzy system with time delay under sampled-data control using a new looped-functional. IEEE Trans. Fuzzy Syst. 28(2), 400–407 (2020)

    Article  Google Scholar 

  9. C. Hua, Y. Wang, S. Wu, Stability analysis of neural networks with time-varying delay using a new augmented Lyapunov–Krasovskii functional. Neurocomputing 332, 1–9 (2019)

    Article  Google Scholar 

  10. O. Kwon, M.J. Park, S. Lee, J.H. Park, Augmented Lyapunov–Krasovskii functional approaches to robust stability criteria for uncertain Takagi–Sugeno fuzzy systems with time-varying delays. Fuzzy Sets Syst. 201, 1–19 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. O. Kwon, M.J. Park, J.H. Park, S. Lee, E.J. Cha, Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov–Krasovskii functional. J. Frankl. Inst. 350(3), 521–540 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. O. Kwon, M.J. Park, J.H. Park, S. 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, 108–122 (2013)

    MathSciNet  MATH  Google Scholar 

  13. K. Li, C. Hua, X. You, X. Guan, Output feedback-based consensus control for nonlinear time delay multiagent systems. Automatica 111, 108669 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  14. Y. Liu, S. Lee, Synchronization criteria of chaotic Lure systems with delayed feedback PD control. Neurocomputing 189, 66–71 (2016)

    Article  Google Scholar 

  15. X. Liu, J. Xia, J. Wang, Interval type-2 fuzzy passive filtering for nonlinear singularly perturbed PDT-switched systems and its application. J. Syst. Sci. Complex 34(6), 2195–2218 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  16. T.H. Lee, J.H. Park, Stability analysis of sampled-data systems via free-matrix-based time-dependent discontinuous Lyapunov approach. IEEE Trans. Automat. Contr. 62(7), 3653–3657 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  17. T.H. Lee, J.H. Park, Improved criteria for sampled-data synchronization of chaotic Lur’e systems using two new approaches. Nonlinear Anal. Hybrid Syst. 24, 132–145 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. S.H. Lee, M.J. Park, O. Kwon, Synchronization criteria for delayed Lur’e systems and randomly occurring sampled-data controller gain. Commun. Nonlinear Sci. Numer. Simul. 68, 203–219 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  19. A. Seuret, C. Briat, Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals. Automatica 55, 274–278 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  20. A. Seuret, F. Gouaisbaut, Hierarchy of LMI conditions for the stability analysis of time-delay systems. Syst. Control. Lett. 81, 1–7 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  21. K. Shi, Y. Tang, X. Liu, S. Zhong, Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lur’e systems with randomly occurring controller gain fluctuation. ISA Trans. 66, 185–199 (2017)

    Article  Google Scholar 

  22. Z. Tang, J.H. Park, H. Shen, Finite-time cluster synchronization of Lur’e networks: A nonsmooth approach. IEEE Trans. Syst. Man Cybern. Syst. 48(8), 1213–1224 (2018)

    Article  Google Scholar 

  23. Z. Tang, J.H. Park, J. Feng, Novel approaches to pin cluster synchronization on complex dynamical networks in Lur’e forms. Commun. Nonlinear Sci. Numer. Simul. 57, 422–438 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  24. T. Wu, J.H. Park, L. Xiong, X. Xie, H. Zhang, A novel approach to synchronization conditions for delayed chaotic Lur’e systems with state sampled-data quantized controller. J. Frankl. Inst. 357(14), 9811–9833 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  25. M. Wang, J. Qiu, M. Chadli, M. Wang, A switched system approach to exponential stabilization of sampled-data T-S fuzzy systems with packet dropouts. IEEE Trans. Cybern. 46(12), 3145–3156 (2015)

    Article  Google Scholar 

  26. J. Wang, J. Xia, H. Shen, M. Xing, J.H. Park, \(H_{\infty } \) Synchronization for fuzzy Markov jump chaotic systems with piecewise-constant transition probabilities subject to PDT switching rule. IEEE Trans. Fuzzy Syst. 29(10), 3082–3092 (2020)

    Article  Google Scholar 

  27. J. Wang, C. Yang, J. Xia, Observer-based sliding mode control for networked fuzzy singularly perturbed systems under weighted try-once-discard protocol. IEEE Trans. Fuzzy Syst. 30, 1889–1899 (2022)

    Article  Google Scholar 

  28. H. Zeng, J.H. Park, S. Xiao, Y. Liu, Further results on sampled-data control for master-slave synchronization of chaotic Lur’e systems with time delay. Nonlinear Dyn. 82(1), 851–863 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  29. H. Zeng, K.L. Teo, Y. He, A new looped-functional for stability analysis of sampled-data systems. Automatica 82, 328–331 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  30. X. Zhang, Q. Han, X. Ge, Sufficient conditions for a class of matrix-valued polynomial inequalities on closed intervals and application to \(H_{\infty }\) filtering for linear systems with time-varying delays. Automatica 125, 109390 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  31. X. Zhang, Q. Han, X. Ge, The construction of augmented Lyapunov-Krasovskii functionals and the estimation of their derivatives in stability analysis of time-delay systems: A survey. Int. J. Syst. Sci. 1-16 (2021)

  32. X. Zhang, Q. Han, X. Ge, Novel stability criteria for linear time-delay systems using Lyapunov–Krasovskii functionals with a cubic polynomial on time-varying delay. IEEE/CAA J. Autom. Sinica 8(1), 77–85 (2021)

    MathSciNet  Google Scholar 

  33. X. Zhang, Q. Han, X. Ge, L. Ding, Resilient control design based on a sampled-data model for a class of networked control systems under denial-of-service attacks. IEEE Trans. Cybern. 50(8), 3616–3626 (2019)

    Article  Google Scholar 

  34. X. Zhang, Q. Han, A. Seuret, F. Gouaisbaut, An improved reciprocally convex inequality and an augmented Lyapunov–Krasovskii functional for stability of linear systems with time-varying delay. Automatica 84, 221–226 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  35. X. Zhang, Q. Han, A. Seuret, F. Gouaisbaut, Y. He, Overview of recent advances in stability of linear systems with time-varying delays. IET Control. Theory Appl. 13(1), 1–16 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  36. X. Zhang, Q. Han, Z. Zeng, Hierarchical type stability criteria for delayed neural networks via canonical Bessel–Legendre inequalities. IEEE Trans. Cybern. 48(5), 1660–1671 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

This paper is partially supported by the National Natural Science Foundation of China (61503120), the Natural Science Foundation of Hebei Province (F2021209006), the Fostering Talents Foundation of North China University of Science and Technology (JP201511), the Project funded by Natural Science Foundation-Steel and Iron Foundation of Hebei Province under Grant (E2019105123), the Science and Technology Project of Hebei Education Department under Grant (ZD2019311) and the Tangshan Talent Funding Project (A2021110015).

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Authors and Affiliations

  1. Institute of Electrical Engineering, North China University of Science and Technology, Tangshan, China

    Chao Ge & Xiaodong Liu

  2. School of Control and Computer Engineering, North China Electric Power University, Beijing, China

    Yajuan Liu

  3. Institute of Electrical Engineering, Yanshan University, Qinhuangdao, China

    Changchun Hua

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  1. Chao Ge
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  2. Xiaodong Liu
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  3. Yajuan Liu
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  4. Changchun Hua
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Correspondence to Chao Ge.

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Ge, C., Liu, X., Liu, Y. et al. Synchronization Stability Criteria for Lur’e Systems via Delay-Product-Type Functional Method. Circuits Syst Signal Process 42, 2088–2106 (2023). https://doi.org/10.1007/s00034-022-02210-4

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