On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms
Optimization and Control
2008-03-08 v2
Abstract
We provide an example proving that there exists no quadratic Lyapunov function for a certain class of linear agreement/consensus algorithms, a fact that had been numerically verified in [5]. We also briefly discuss sufficient conditions for the existence of such a Lyapunov function.
Keywords
Cite
@article{arxiv.0706.2876,
title = {On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms},
author = {Alex Olshevsky and John N. Tsitsiklis},
journal= {arXiv preprint arXiv:0706.2876},
year = {2008}
}