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- W2352917942 abstract "This paper addresses the convergence of infinite product of matrices.By extending the paracontracting matrix notion in the existing literature,we propose the concept of uniformly paracontracting set and develop some interesting properties of it.Based on these properties,we prove a result by the Bolzano-Weierstrass theorem that any infinite matrices product chosen from a uniformly paracontracting set is convergent.Moreover,the construction of the limit matrix is explicitly presented as well.This result includes and improves the existing results on the convergence of infinite product of finite paracontracting matrices.With the obtained result,we study the consensus problem of the Vicsek model with time-varying Laplacian matrix.In a new way,a consensus result based on a nearest neighbor rule is proved that all the particles in the Vicsek model will eventually move in the same direction provided that the topology is jointly connected over any infinite interval." @default.
- W2352917942 created "2016-06-24" @default.
- W2352917942 creator A5072395485 @default.
- W2352917942 date "2013-01-01" @default.
- W2352917942 modified "2023-09-27" @default.
- W2352917942 title "THE CONVERGENCE OF INFINITE PRODUCT OF UNIFORMLY PARACONTRACTING MATRICES AND ITS APPLICATION IN CONSENSUS OF THE VICSEK MODEL" @default.
- W2352917942 hasPublicationYear "2013" @default.
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