Delay-Independent Stability of Consensus Networks with Application to Flocking^∗

Abstract

This work studies a class of linear first order and non-linear second order static distributed consensus networks with time-varying multiple propagation delays, in continuous time. We provide conditions for convergence of to a common constant value, under an increased connectivity condition. The results are delay-independent in the sense that they hold for arbitrary bounded delays. Our approach makes use of fundamental concepts from the Non-Negative Matrix Theory in a fairly elementary way.