  In this paper, we discuss pinning consensus in networks of multiagents via
impulsive controllers. In particular, we consider the case of using only one
impulsive controller. We provide a sufficient condition to pin the network to a
prescribed value. It is rigorously proven that in case the underlying graph of
the network has spanning trees, the network can reach consensus on the
prescribed value when the impulsive controller is imposed on the root with
appropriate impulsive strength and impulse intervals. Interestingly, we find
that the permissible range of the impulsive strength completely depends on the
left eigenvector of the graph Laplacian corresponding to the zero eigenvalue
and the pinning node we choose. The impulses can be very sparse, with the
impulsive intervals being lower bounded. Examples with numerical simulations
are also provided to illustrate the theoretical results.
