Abstract
In this article, we consider time-varying distributed averaging dynamics. Motivated by a necessary condition on the ergodicity, we provide a sufficient condition for the ergodicity of such dynamics. We show that if groups of agents are connected using a directed acyclic graph containing a spanning directed rooted tree and the averaging dynamics restricted to each group is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {P}^*$</tex-math></inline-formula> , then the dynamics over the whole network is ergodic. In particular, this provides a general condition for convergence of consensus dynamics where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> groups <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> of agents capable of reaching consensus follow each other on a time-varying network.
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