Onur CİHAN, Mehmet AKAR

Effect of nonuniform varying delay on the rate of convergence in averaging-based consensus

This paper discusses the effect of nonuniform varying communication delay on distributed consensus algorithms in discrete time. After introducing the delayed mathematical model, we first investigate the ergodicity of the delayed system using the properties of scrambling matrices. Subsequently, the effect of nonuniform varying delay on convergence is examined. It is shown theoretically that nonuniform delay is not detrimental to the convergence rate of the algorithm for directed acyclic graphs. The results are also illustrated with several numerical examples.

Anahtar Kelimeler:

Consensus, distributed control, networks with time delays

Effect of nonuniform varying delay on the rate of convergence in averaging-based consensus

Keywords:

Consensus, distributed control, networks with time delays,

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which implies that the nonzero spectra of pk( ˆA) and Akare equal to each other. For 1≤ k < τmax, the first k subrows of pk( ˆA) have the form    . . .. ∗ . . . ∗ AD+∗
whereas the last τmax+ 1− k subrows are equal to [I(τmax+1−k)n0] , where I(τmax+1−k)nis the identity matrix of length (τmax+ 1− k)n. The same recursive procedure as above can be applied to pk( ˆA) in this case as well to obtain the desired result.