Necessary and sufficient conditions for asymptotic swarm stability of high order swarm systems

In this paper, the asymptotic swarm stability problem of high order swarm systems is dealt with. The concept of swarm stability is formally defined based on consensus. Necessary and sufficient conditions for asymptotic swarm stability are respectively presented for two types of swarm systems. The first type is LTI, while the second is nonlinear time-varying. For general LTI systems, the condition depends on the graph topology, the dynamics of agents and the interactions among the neighbors; while for curtain nonlinear time-varying systems, the condition is determined by two independent aspects: agent attraction and graph connection.