Characterization of link failures in multi-agent systems under the agreement protocol

The concept of detectability for a link with respect to an agent in a multi-agent system is introduced in this work. Link failures in the network are characterized in terms of their detectability, depending on how a link failure affects the response of a particular node in the system, and whether the link failure can be determined by observing that node´s response. Sufficient conditions for detectability are provided and it is pointed out that link failures are detectable for a class of directed graphs with rooted out-branchings. The conceptually related notion of distinguishable directed information flow graphs is also introduced, and its importance in a multi-agent system is discussed. Simulation studies reveal that the obtained analytical results hold for randomly initialized network configurations.