  We derive necessary and sufficient conditions for leader-follower multi-agent
systems such that we can further apply prescribed performance control to
achieve the desired formation while satisfying certain transient constraints. A
leader-follower framework is considered in the sense that a group of agents
with external inputs are selected as leaders in order to drive the group of
followers in a way that the entire system can achieve target formation within
certain prescribed performance transient bounds. We first derive necessary
conditions on the leader-follower graph topology under which the target
formation together with the prescribed performance guarantees can be fulfilled.
Afterwards, the derived necessary conditions are extended to necessary and
sufficient conditions for leader-follower formation control under transient
constraints. Finally, the proposed results are illustrated with simulation
examples.
