  In this paper, we study the cooperative output regulation problem for the
discrete linear time-delay multi-agent systems by distributed observer
approach. In contrast with the same problem for continuous-time linear
time-delay multi-agent systems, the problem has two new features. First, in the
presence of time-delay, the regulator equations for discrete-time linear
systems are different from those for continuous-time linear systems. Second,
under the standard assumption on the connectivity of the communication graph, a
distributed observer for any continuous-time linear leader system always
exists. However, this is not the case for discrete-time systems, and the
behavior of a distributed observer is much more complicated. Thus, we will
first study the existence of the discrete distributed observer, and then
present the solvability of the problem by distributed dynamic output feedback
control law.
