<p>This paper is dedicated to fixed-time passivity and synchronization for multi-weighted spatiotemporal directed networks. First, to achieve fixed-time passivity, a type of decentralized power-law controller is developed, in which only one parameter needs to be adjusted in the power-law terms; this greatly decreases the inconvenience of parameter adjustment. Second, several fixed-time passivity criteria with LMI forms are derived by using a Gauss divergence theorem to deal with the spatial diffusion of nodes and by applying the Hölder’s inequality to dispose rigorously the power-law term greater than one in the designed control scheme; this improves the previous theoretical analysis. Additionally, the fixed-time synchronization of spatiotemporal directed networks with multi-weights is addressed as a direct result of fixed-time strict passivity. Finally, a numerical example is presented in order to show the validity of the theoretical analysis.</p>

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Fixed-time passivity and synchronization of spatiotemporal directed networks with multiple weights

  • Yujie Ma,
  • Cheng Hu,
  • Leimin Wang

摘要

This paper is dedicated to fixed-time passivity and synchronization for multi-weighted spatiotemporal directed networks. First, to achieve fixed-time passivity, a type of decentralized power-law controller is developed, in which only one parameter needs to be adjusted in the power-law terms; this greatly decreases the inconvenience of parameter adjustment. Second, several fixed-time passivity criteria with LMI forms are derived by using a Gauss divergence theorem to deal with the spatial diffusion of nodes and by applying the Hölder’s inequality to dispose rigorously the power-law term greater than one in the designed control scheme; this improves the previous theoretical analysis. Additionally, the fixed-time synchronization of spatiotemporal directed networks with multi-weights is addressed as a direct result of fixed-time strict passivity. Finally, a numerical example is presented in order to show the validity of the theoretical analysis.