  The objective of the invariant ellipsoid method is to minimize the smallest
invariant and attractive set of a linear control system operating under the
influence of bounded external disturbances. In this paper, this method is
extended into the leader-following consensus problem. Initially, a linear
control protocol is designed for the Multi-agent System without disturbances.
Subsequently, in the presence of bounded disturbances, by employing a similar
linear control protocol, a necessary and sufficient condition is introduced to
derive the optimal control parameters for the MAS such that the state of
followers converge and remain in an minimal invariant ellipsoid around the
state of the leader.
