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arXiv · 1407.7585

Lyapunov Approach to Consensus Problems

Angelia Nedich·Ji Liu
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Abstract

This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the behavior of weighted-averaging dynamic. As a result, new convergence rate results are obtained that capture the graph structure in a novel way. In particular, the exponential convergence rate is established for unconstrained consensus with the exponent of the order of $1-O(1/(m\log_2m))$. Also, the exponential convergence rate is established for constrained consensus, which extends the existing results limited to the use of doubly stochastic weight matrices.

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Angelia Nedich, Ji Liu. 2014-07-28. Lyapunov Approach to Consensus Problems. https://arxiv.org/abs/1407.7585

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