We prove that for a set of communicating agents to compute the average of
their initial positions (average consensus problem), the optimal topology of
communication is given by a de Bruijn's graph. Consensus is then reached in a
finitely many steps. A more general family of strategies, constructed by block
Kronecker products, is investigated and compared to Cayley strategies.Comment: 9 pages; extended preprint with proofs of a CDC 2007 (Conference on
decision and Control) pape
