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The impulsive synchronization of multiplex networks with mixed delays and dual uncertainties

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  • Liu, Shuang
  • Xu, Tianwei
  • Wang, Qingyun
  • Yang, Yan

Abstract

The investigation of impulsive synchronization in multiplex Lur'e networks with heterogeneity is presented. In the multiplex network, each layer of the network shares nodes, and each layer topology is a directed spanning tree with root nodes. Thus the pinning control strategy under the leader-following mechanism is adopted. The network structure is multiplex, and thus uncertainties and time delays are inevitable. By the aid of Schur complement lemma, the uncertain terms for linear and nonlinear parameters, as well as for the coupling, are introduced to account for the effects of these uncertainties on the stability of the system. Moreover, both node delays and coupling delays are considered and addressed with the comparison theorem. Based on the stability theory, several conditions for quasi-synchronization are formulated, and the error bound is computed. Furthermore, when the approach is generalized to systems with parameter perturbations and delays, analogous conclusions can still be obtained. Finally, two examples are conducted to demonstrate the control protocol's efficacy.

Suggested Citation

  • Liu, Shuang & Xu, Tianwei & Wang, Qingyun & Yang, Yan, 2024. "The impulsive synchronization of multiplex networks with mixed delays and dual uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 141-163.
    • Handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:141-163
    DOI: 10.1016/j.matcom.2023.12.013
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