  This paper considers the distributed robust control problems of uncertain
linear multi-agent systems with undirected communication topologies. It is
assumed that the agents have identical nominal dynamics while subject to
different norm-bounded parameter uncertainties, leading to weakly heterogeneous
multi-agent systems. Distributed controllers are designed for both continuous-
and discrete-time multi-agent systems, based on the relative states of
neighboring agents and a subset of absolute states of the agents. It is shown
for both the continuous- and discrete-time cases that the distributed robust
control problems under such controllers in the sense of quadratic stability are
equivalent to the $H_\infty$ control problems of a set of decoupled linear
systems having the same dimensions as a single agent. A two-step algorithm is
presented to construct the distributed controller for the continuous-time case,
which does not involve any conservatism and meanwhile decouples the feedback
gain design from the communication topology. Furthermore, a sufficient
existence condition in terms of linear matrix inequalities is derived for the
distributed discrete-time controller. Finally, the distributed robust
$H_\infty$ control problems of uncertain linear multi-agent systems subject to
external disturbances are discussed.
