Consensus over directed graph: Output feedback and topological constraints

In this paper, the discrete-time multi-agent systems consensus problem over a directed, fixed network communication graph is studied. A distributed dynamic output feedback control protocol is employed. Drawing upon concepts and techniques from robust control, notably those concerning gain-phase margin optimization and analytic interpolation, we obtained explicit sufficient conditions for general linear agents to achieve consensus. The results display an explicit dependence of the consensus condition on the agent´s unstable poles, non-minimum phase zeros and their relative degree.