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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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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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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DOI: https://doi.org/10.1007/s00034-022-02210-4