FIXED-TIME PASSIVITY AND SYNCHRONIZATION OF SPATIOTEMPORAL DIRECTED NETWORKS WITH MULTIPLE WEIGHTS

doi:10.1007/s10473-026-0120-7

Abstract

Abstract: 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.

Key words: fixed-time passivity, fixed-time synchronization, spatiotemporal networks, multiple weights, directed topology

CLC Number:

93B52

Yujie MA¹, Cheng HU^1,*, Leimin WANG². FIXED-TIME PASSIVITY AND SYNCHRONIZATION OF SPATIOTEMPORAL DIRECTED NETWORKS WITH MULTIPLE WEIGHTS[J].Acta mathematica scientia,Series B, 2026, 46(1): 361-382.

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