A Necessary and Sufficient Condition for Consensus Over Random Networks
Coauthor(s): Ali Jadbabaie.
We consider the consensus problem for stochastic discrete-time linear dynamical systems. The underlying graph of such systems at a
given time instance is derived from a random graph process, independent of other time instances. For such a framework, we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. This easily verifiable condition uses the spectrum of the average weight matrix. Finally, we investigate a special case for which the linear dynamical system converges to a fixed vector with
Source: IEEE Transsactions on Automatic Control
Tahbaz-Salehi, Alireza, and Ali Jadbabaie. "A Necessary and Sufficient Condition for Consensus Over Random Networks." IEEE Transsactions on Automatic Control 53, no. 3 (April 2008): 791-795.