Mathematical Control Theory

Discrete consensus convergence procedure via minimal cycle combining strong components

R. P. Agaev

Institute of Control Sciences of RAS

Abstract: This paper is devoted to consensus problems in discrete multi-agent systems whose communication digraphs consist of disjoint strong components. It is shown that any block in the power limit of a decomposable and aperiodic influence matrix $P$ of a digraph $\Gamma$ is proportional to the corresponding block in the power limit of the influence matrix of the digraph $\Gamma^h$ obtained from $\Gamma$ by combining the strong components by means of a minimal cycle. It is proved that for some arc weights in this minimal cycle, the power limit of the influence matrix of $\Gamma^h$ coincides with the resulting matrix of the orthogonal projection procedure applied to $\Gamma$.

Keywords: multi-agent systems, decentralized control, communication digraph, consensus, Laplacian matrix, Kirchhoff matrix, DeGroot model, control.

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