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 |
ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization
Fingerprint Dive into the research topics of 'Stability of a distributed algorithm for solving linear algebraic equations'. Together they form a unique fingerprint.
Cite this
Liu, J., Morse, A. S., Nedic, A., & Basar, T. (2014). Stability of a distributed algorithm for solving linear algebraic equations. Proceedings of the IEEE Conference on Decision and Control, 2015-February(February), 3707-3712. [7039966]. https://doi.org/10.1109/CDC.2014.7039966