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Consensus analysis of double integrator agents with persistent interaction graphs

This article proposes a technique to compute convergence rate to consensus for multi-agent systems with double integrator agent dynamics interacting via time-varying, undirected and persistent communication graphs. Existing results provide control laws guaranteeing asymptotic convergence to consensus but no practically computable estimate of the convergence rate. We introduce a novel analysis technique relying on classical notions of persistent of excitation (PE) to establish the convergence rate of a mildly modified double integrator consensus law. Since the individual time-varying weights pass through singularities, the closed loop agent dynamics correspond to a time-varying linear system. A transformation is utilized to convert the consensus problem into a stabilization problem on which an amalgamation of the potential function approach and persistence of excitation (PE) results are applied. As in the single integrator case [1], a saturation in the convergence rate is observed.