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We study continuous-time consensus dynamics for multi-agent systems withundirected switching interaction graphs. We establish a necessary andsufficient condition for exponential asymptotic consensus based on theclassical theory of complete observability. The proof is remarkably simplecompared to similar results in the literature and the conditions for consensusare mild. This observability-based method can also be applied to the case wherenegatively weighted edges are present. Additionally, as a by-product of theobservability based arguments, we show that the nodes' initial value can berecovered from the signals on the edges up to a shift of the network average.

Convergence and State Reconstruction of Time-varying Multi-agent Systems from Complete Observability Theory