Performance Improvement in Noisy Linear Consensus Networks With Time-Delay

We analyze performance of a class of time-delay first-order consensus networks from a graph topological perspective and present methods to improve it. Performance is measured by network's square of H
₂
norm and it is derived in closed form. Moreover, we prove that performance is a convex function of the coupling weights of the underlying graph. We demonstrate that the effect of time-delay reincarnates itself in the form of non-monotonicity, leading to counter-intuitive behaviors of the performance as a function of graph topology. For the network design problem, we propose a tight but simple approximation of the performance measure in order to achieve lower complexity in our problems by eliminating the computationally expensive need for eigendecomposition. More specifically, we discuss three H
₂
-based optimal design methods to enhance performance. The proposed algorithms provide near-optimal solutions with improved computational complexity as opposed to existing methods in the literature.