We consider a formation of vehicles moving on the two dimensional plane. The
movement of each vehicle is described by
a system of ordinary differential equations with inputs. The formation is maintained
using autonomous controls that are
designed to maintain ﬁxed relative distances and orientations between vehicles.
Moreover this formation should track a given
trajectory on the plane. The vehicles can measure the relative distances and angles to
their neighbors. These values are the
inputs from one system to another. With the help of a general ISS small-gain theorem for
networks we will show that the
dynamics of such a formation is stable for the given controls. The notion of local input-
to- state stability (local ISS) will be
used for this purpose.