  This paper addresses the distributed consensus design problem for linear
multi-agent systems with directed communication graphs and external
disturbances. Both the cases with strongly connected communication graphs and
leader-follower graphs containing a directed spanning tree with the leader as
the root are discussed. Distributed adaptive consensus protocols based on the
relative states of neighboring agents are designed, which can ensure the
ultimate boundedness of the consensus error and adaptive gains in the presence
of external disturbances. The upper bounds of the consensus error are further
explicitly given. Compared to the existing consensus protocols, the merit of
the adaptive protocols proposed in this paper is that they can be computed and
implemented in a fully distributed fashion and meanwhile are robust with
respect to external disturbances.
