Stability analysis of flocking for multi-agent dynamic systems (Q1940730)

The authors first show that the cohesion condition given in [\textit{R. Olfati-Saber} and \textit{R. M. Murray}, ``Consensus problems in networks of agents with switching topology and time-delays'', IEEE Trans. Automat. Control 49, 1520--1533 (2004; \url{doi:10.1109/TAC.2004.834113})] is implied under a mild assumption on the connectivity of graphs. They analyze the stability of flocking. Sufficient conditions are established to guarantee the emergence of flocking with \(\alpha\)-lattice. For the case when there is a leader rather than a virtual leader among agents, they propose a flocking algorithm and analyze the emergence of flocking with \(\alpha\)-lattice. It is also worth pointing out that the LaSalle invariance principle is used to establish the main results under the assumption that there is only a joint path from one agent to any other agent across \([t_0,t_0+T]\) for any \(t_0>0\) and some \(T>0\) in the moving frame. This requires a careful examination due to the boundedness of trajectories.