A comparative study of persistence based convergence rate estimates to consensus

This article presents a comparative study of convergence rate estimates for degenerate gradient flows in the context of multi-agent systems. A novel analysis methodology was introduced in (Roy Chowdhury and Srikant, 2014) based on the classical notions of persistence of excitation (PE) and uniform complete observability (UCO) to study the exponential stability of consensus protocol with time-varying agent dynamics. The new technique allowed precise computation of the convergence rate for single integrator agent dynamics. The purpose of this article is principally twofold. Firstly, we revisit the continuous time spanning edge agent dynamics proposed in (Roy Chowdhury and Srikant, 2014) and present a different analysis approach to study the convergence property for the same. Our analysis mimics the recent result by Brockett (Brockett, 2000) on single agent adaptive control. Secondly, the convergence rate estimates arrived at from the two approaches are compared. Simulations on different examples are provided to elucidate the main theoretical contribution.