Abstract-We consider the problem of fault detection and isolation for a class of linear dynamical systems defined by a graph containing faulty vertices and observer vertices. Using a geometric approach, we provide a characterization of the smallest conditioned invariant subspaces generated by faults in terms of the underlying graph structure. Based on this characterization, we give graph-theoretic conditions guaranteeing fault detectability. In addition, we provide a condition under which fault detectability fails.

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This paper studies consensus problems for multi-agent systems defined on directed graphs where the consensus dynamics involves general nonlinear and discontinuous functions. Sufficient conditions, only involving basic properties of the nonlinear functions and the topology of the underlying graph, are derived for the agents to converge to consensus.

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