Cooperative output regulation of discrete‐time linear time‐delay multi‐agent systems

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 the discrete counterpart of the distributed observer for the continuous‐time systems. Another type of discrete distributed observer is proposed. It turns out that such an observer always exists under some mild assumptions. Using this result, the authors further present the solvability conditions of the problem by distributed dynamic output feedback control law.