  This paper studies the problem of stabilizing target formations specified by
inter-neighbor bearings with relative position measurements. While the
undirected case has been studied in the existing works, this paper focuses on
the case where the interaction topology is directed. It is shown that a linear
distributed control law, which was proposed previously for undirected cases,
can still be applied to the directed case. The formation stability in the
directed case, however, relies on a new notion termed bearing persistence,
which describes whether or not the directed underlying graph is persistent with
the bearing rigidity of a formation. If a target formation is not bearing
persistent, undesired equilibriums will appear and global formation stability
cannot be guaranteed. The notion of bearing persistence is defined by the
bearing Laplacian matrix and illustrated by simulation examples.
