Matrix analysis
Spanning Forests of a Digraph and Their Applications
Automation and Remote Control
On Determining the Eigenprojection and Components of a Matrix
Automation and Remote Control
Google's PageRank and Beyond: The Science of Search Engine Rankings
Google's PageRank and Beyond: The Science of Search Engine Rankings
Coordination in multiagent systems and Laplacian spectra of digraphs
Automation and Remote Control
Distributed Consensus in Multi-vehicle Cooperative Control: Theory and Applications
Distributed Consensus in Multi-vehicle Cooperative Control: Theory and Applications
Social and Economic Networks
Evolution and dynamics of complex networks of coupled systems
IEEE Circuits and Systems Magazine - Special issue on complex networks applications in circuits and systems
Dynamic models of informational control in social networks
Automation and Remote Control
Addendum to the paper "On Determining the Eigenprojection and Components of a Matrix"
Automation and Remote Control
A cyclic representation of discrete coordination procedures
Automation and Remote Control
Regularization-based solution of the PageRank problem for large matrices
Automation and Remote Control
Automation and Remote Control
On the convergence domain in the differential model of reaching a consensus
Automation and Remote Control
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In the coordination/consensus problem for multi-agent systems, a well-known condition of achieving consensus is the presence of a spanning arborescence in the communication digraph. The paper deals with the discrete consensus problem in the case where this condition is not satisfied. A characterization of the subspace T P of initial opinions (where P is the influence matrix) that ensure consensus in the DeGroot model is given. We propose a method of coordination that consists of: (1) the transformation of the vector of initial opinions into a vector belonging to T P by orthogonal projection and (2) subsequent iterations of the transformation P. The properties of this method are studied. It is shown that for any non-periodic stochastic matrix P, the resulting matrix of the orthogonal projection method can be treated as a regularized power limit of P.