  The problem of disturbance rejection/attenuation for constant-input delayed
linear multi-agent systems (MASs) with the directed communication topology is
tackled in this paper, where a classic model reduction technique is introduced
to transform the delayed MAS into the delay-free one. First, when the leader
has no control input, a novel adaptive predictive extended state observer (ESO)
using only relative state information of neighboring agents is designed to
achieve disturbance-rejected consensus tracking. The stabilization analysis is
presented via the Lyapunov function and sufficient conditions are derived in
terms of linear matrix inequalities. Then the result is extended to the
disturbance-attenuated case where the leader has bounded control input which is
only known by a portion of followers. Finally, two numerical examples are
presented to illustrate the effectiveness of proposed strategies. The main
contribution focuses on the design of adaptive predictive ESO protocols with
the fully distributed property.
