### Abstract

In [1], given a matrix A and a vector b, a distributed algorithm was proposed for solving linear algebraic equations of the form Ax = b when there is at least one solution. The equation is simultaneously solved by a group of autonomous agents whose neighbor relations are characterized by a time-dependent directed graph. The main contribution of this paper is to provide necessary and sufficient conditions for exponential convergence of the algorithm under the most general assumption. These conditions utilize a new notion of graph connectivity which is less restrictive than strong connectivity.

Original language | English (US) |
---|---|

Article number | 7039966 |

Pages (from-to) | 3707-3712 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 2015-February |

Issue number | February |

DOIs | |

State | Published - Jan 1 2014 |

Event | 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*,

*2015-February*(February), 3707-3712. [7039966]. https://doi.org/10.1109/CDC.2014.7039966

**Stability of a distributed algorithm for solving linear algebraic equations.** / Liu, Ji; Morse, A. Stephen; Nedic, Angelia; Basar, Tamer.

Research output: Contribution to journal › Conference article

*Proceedings of the IEEE Conference on Decision and Control*, vol. 2015-February, no. February, 7039966, pp. 3707-3712. https://doi.org/10.1109/CDC.2014.7039966

}

TY - JOUR

T1 - Stability of a distributed algorithm for solving linear algebraic equations

AU - Liu, Ji

AU - Morse, A. Stephen

AU - Nedic, Angelia

AU - Basar, Tamer

PY - 2014/1/1

Y1 - 2014/1/1

N2 - In [1], given a matrix A and a vector b, a distributed algorithm was proposed for solving linear algebraic equations of the form Ax = b when there is at least one solution. The equation is simultaneously solved by a group of autonomous agents whose neighbor relations are characterized by a time-dependent directed graph. The main contribution of this paper is to provide necessary and sufficient conditions for exponential convergence of the algorithm under the most general assumption. These conditions utilize a new notion of graph connectivity which is less restrictive than strong connectivity.

AB - In [1], given a matrix A and a vector b, a distributed algorithm was proposed for solving linear algebraic equations of the form Ax = b when there is at least one solution. The equation is simultaneously solved by a group of autonomous agents whose neighbor relations are characterized by a time-dependent directed graph. The main contribution of this paper is to provide necessary and sufficient conditions for exponential convergence of the algorithm under the most general assumption. These conditions utilize a new notion of graph connectivity which is less restrictive than strong connectivity.

UR - http://www.scopus.com/inward/record.url?scp=84988289973&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988289973&partnerID=8YFLogxK

U2 - 10.1109/CDC.2014.7039966

DO - 10.1109/CDC.2014.7039966

M3 - Conference article

AN - SCOPUS:84988289973

VL - 2015-February

SP - 3707

EP - 3712

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

IS - February

M1 - 7039966

ER -