  Linear consensus iterations guarantee asymptotic convergence, thereby,
limiting their applicability in applications where consensus value needs to be
used in real time to perform a system level task. It also leads to wastage of
power and communication resources. In this article, an algorithm is proposed
which enables each node to detect in a distributed manner and in finite number
of iterations, when every agent in the network is within a user specified
threshold of the consensus value (approximate consensus) and hence terminate
further communications and computations associated with consensus iterations.
This article develops a distributed algorithm for achieving this approximate
consensus in presence of random time-varying bounded communication delays.
Moreover, the article instantiates the algorithm developed to distributively
determine the average of the initial values held by agents in finite number of
iterations. Specifically, this algorithm relies on distributively determining
the maximum and minimum of values held by the agents. The approach presented
here offers several advantages, including reduced computational complexity, and
hence, is suited for hardware implementation. An experimental test bed of
Raspberry-Pi agents that communicate wirelessly over neighborhoods is employed
as a platform to demonstrate the effectiveness of the developed algorithm.
