## Abstract

We propose two distributed algorithms, one for solving the weight-balance problem and another for solving the bistochastic matrix formation problem, in a distributed system whose components (nodes) can exchange information via interconnection links (edges) that form an arbitrary, possibly directed, strongly connected communication topology (digraph). Both distributed algorithms achieve their goal asymptotically and operate iteratively by having each node adapt the (nonnegative) weights on its outgoing edges based on the weights of its incoming links.The weight-balancing algorithm is shown to admit geometric convergence rate, whereas the second algorithm, which is a modification of the weight-balancing algorithm, leads asymptotically to a bistochastic digraph with geometric convergence rate for a certain set of initial values. The two algorithms perform better than existing approaches, as illustrated by the examples we provide.

Original language | English |
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Title of host publication | 2013 European Control Conference, ECC 2013 |

Pages | 1752-1757 |

Number of pages | 6 |

Publication status | Published - 2013 |

MoE publication type | A4 Article in a conference publication |

Event | European Control Conference - ETH Zurich, Zurich, Switzerland Duration: 17 Jul 2013 → 19 Jul 2013 |

### Conference

Conference | European Control Conference |
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Abbreviated title | ECC |

Country/Territory | Switzerland |

City | Zurich |

Period | 17/07/2013 → 19/07/2013 |