On the properties of orthogonal projection method for reaching consensus

The article is devoted to an asymptotic behavior of a multi-agent system with information links. We proved that the orthogonal projection method proposed for the regularization of the consensus protocol is characterized by a pseudoinverse matrix for the introduced auxiliary matrix for an arbitrary communication digraph of a multi-agent system. We cosidered the eigenprojection of the Laplacian matrix corresponding to the communication digraph, in which the influences on the fixed agent change proportionally. We obtained a number of results that are of independent importance and can be used in models of multi-agent systems with different protocols.