## Alireza Tahbaz-Salehi

*A Necessary and Sufficient Condition for Consensus Over Random Networks*

Coauthor(s): Ali Jadbabaie.

**Abstract:**

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
probability 1.

**Source:** *IEEE Transsactions on Automatic Control*

**Exact Citation:**

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.

**Volume:** 53

**Number:** 3

**Pages:** 791-795

**Date:**
4
2008