Consensus of linear time-varying multi-agent systems with a variable number of nodes

This study explores the consensus problem for open multi-agent systems (MASs) characterized by agents with linear time-varying (LTV) dynamics under switching topology with a variable number of nodes. The consensus problem of MASs with different switching topologies and varying node numbers is solved by constructing the augmented Laplacian matrices and the averaging theory. Unlike most of the existing literature, the average uniform connectivity of the graph is only required in this paper, and the topology at any time can be disconnected. Furthermore, our solution extends to the simplified scenario of MASs with linear time-invariant (LTI) dynamics’ agents, as well as the switching topology with a fixed number of nodes. Finally, the effectiveness and superiority of our theoretical findings are validated through simulation examples.