Distributed consensus for agents with independent position and velocity interactions

We consider the consensus for multiple double-integrator agents systems in a general framework that the position and velocity interactions among agents are modeled by independent graphs. Different algorithms are proposed and analyzed for various different settings, including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies, as well as the case with a group velocity reference signal under switching velocity interaction. Rigorous convergence analysis are preformed via a combined use of tools from algebraic graph theory, matrix analysis as well as the advanced Lypapunov stability theory.