On the stability and convergence of a class of consensus systems with a nonlinear input

We consider a class of consensus systems driven by a nonlinear input. Such systems arise in a class of Internet of Things (IOT) applications. Our objective in this paper is to determine conditions under which a certain partially distributed system converges to a Lur'e-like scalar system, and to provide a rigorous proof of its stability. Conditions are derived for the non-uniform convergence and stability of such a system and an example is given of a speed advisory system where such a system arises.