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Synchronization of Coupled Neutral-Type Delay Partial Differential Systems

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Abstract

This paper considers the asymptotical synchronization and \(H_\infty \) synchronization for coupled neutral-type delay partial differential systems (NDPDSs). First, we construct a coupled synchronization error dynamic. Using the method of nonsingular matrix transformation, we decouple these coupled synchronization error dynamical systems. Then we study the asymptotical stability of the decoupled synchronization error dynamical systems through the Lyapunov–Krasovskii functional method, which implies the asymptotical synchronization of the coupled NDPDSs. Furthermore, when external disturbances enter the coupled NDPDSs, the \(H_\infty \) synchronization problem is also considered. The equivalence between the \(H_\infty \) stability of decoupled synchronization error dynamical systems and the \(H_\infty \) synchronization of coupled NDPDSs is proved by rigorous mathematical analysis. Then the criterion for the \(H_\infty \) stabilization is presented, which guarantees the \(H_\infty \) synchronization of the coupled NDPDSs. Moreover, as a remarkable difference between the ordinary differential systems and partial differential systems, the effect of the spatial domain on the synchronization is revealed through the obtained criteria. At last, numerical examples are given to illustrate the correctness of our results.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant 61074160 and the Natural Scientific Foundation of Shandong Province under Grant ZR2014FQ014, the Program for IBRSEM in Harbin Institute of Technology under Grant HIT.IBRSEM.A.201415, and the Foundation of Supporting Technology for Aerospace under Grant 2014-HT-HGD7.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, 264209, People’s Republic of China

    Kai-Ning Wu & Bing-Xin Zhao

  2. Control and Simulation Center, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Yu Yao

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  1. Kai-Ning Wu
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Correspondence to Kai-Ning Wu.

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Wu, KN., Zhao, BX. & Yao, Y. Synchronization of Coupled Neutral-Type Delay Partial Differential Systems. Circuits Syst Signal Process 35, 443–458 (2016). https://doi.org/10.1007/s00034-015-0072-y

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