  This paper studies the consensus problem of general linear discrete-time
multi-agent systems (MAS) with input constraints and bounded time-varying
communication delays. We propose a robust distributed model predictive control
(DMPC) consensus protocol that integrates the offline consensus design with
online DMPC optimization to exploit their respective advantages. More
precisely, each agent is equipped with an offline consensus protocol, which is
a priori designed, depending on its immediate neighbors' estimated states.
Further, the estimation errors propagated over time due to inexact neighboring
information are proved bounded under mild technical assumptions, based on which
a robust DMPC strategy is deliberately designed to achieve robust consensus
while satisfying input constraints. Moreover, it is shown that, with the
suitably designed cost function and constraints, the feasibility of the
associated optimization problem can be recursively ensured. We further provide
the consensus convergence result of the constrained MAS in the presence of
bounded varying delays. Finally, two numerical examples are given to verify the
effectiveness of the proposed distributed consensus algorithm.
