Topological constraints on consensus via delayed output feedback over directed graph

This paper is devoted to the consensusability of discrete-time linear time invariant (LTI) multi-agent systems over a fixed directed network communication graph. A distributed dynamic output feedback control protocol is employed and the each agent´s input is assumed to be subjected to a constant unknown time delay. Drawing upon the phase margin and gain-phase margin optimization concepts as well as analytic interpolation techniques from robust control, we develop an explicit consensusability conditions of discrete-time LTI agents which provides a limit on network topology imposed by the agent´s unstable poles, non-minimum phase zeros, relative degree and communication time delay. This result also suggests that delayed communication between the LTI agents will generally hinder consensus.