Title: Performance Improvement in Noisy Linear Consensus Networks with Time-Delay,
Abstract: We analyze performance of a class of time-delay first-order consensus
networks from a graph topological perspective and present methods to improve
it. The performance is measured by network's square of H-2 norm and it is shown
that it is a convex function of Laplacian eigenvalues and the coupling weights
of the underlying graph of the network. First, we propose a tight convex, but
simple, approximation of the performance measure in order to achieve lower
complexity in our design problems by eliminating the need for
eigen-decomposition. The effect of time-delay reincarnates itself in the form
of non-monotonicity, which results in nonintuitive behaviors of the performance
as a function of graph topology. Next, we present three methods to improve the
performance by growing, re-weighting, or sparsifying the underlying graph of
the network. It is shown that our suggested algorithms provide near-optimal
solutions with lower complexity with respect to existing methods in literature.