## Abstract

We present a class of consensus protocols over groups of agents with stochastically switching, directed, and weighted communication topologies. In this protocol, an agent's traits, that is, the cardinality of its neighbor set and the weight assigned to its neighbors in the updating process, are given by two jointly distributed random variables and the neighbors of an agent are selected with equal probability. We provide closed form results for the asymptotic convergence rate and for the steady state mean square deviation in the presence of additive noise. These results are specialized to consensus protocols based on Erds-Rényi and numerosity-constrained networks.

Original language | English (US) |
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Pages (from-to) | 221-235 |

Number of pages | 15 |

Journal | Linear Algebra and Its Applications |

Volume | 437 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1 2012 |

## Keywords

- Consensus protocol
- Convergence rate
- Directed network
- Random topology
- Stochastic stability

## ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics