Convergence rate analysis for discrete-time multi-agent systems with time-varying delays

Over the past decade, an increasing amount of interest has centered around the consensus (or synchronization) problem of multi-agent systems (MASs). Although there are numerous results reported on the convergence of an MAS based on the product of an infinite sequence of matrices with a uniform lower bound for all nonzero entries, few are on the convergence rate of the MAS. Estimation of the convergence rate is very often important but also a challenging task. This paper proposes an approach to analyze the convergence rate of discrete-time MASs in the presence of time-varying delays. We obtain an upper bound on the convergence rate under the condition of joint connectivity. Our proposed approach does not require the assumption of uniform lower bound for all nonzero entries of the matrices.