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This paper extends a synchronization criterion established for networks offinite-dimensional linear systems to the infinite-dimensional setting. Ourresult, established in the general framework of input-output relations,requires an additional input-output stability property, compared to thefinite-dimensional counterpart. We establish conditions for this property tohold for a large class of infinite-dimensional systems including AbstractCauchy Problems, parabolic PDEs, and time-delay ordinary differentialequations.

An input-output framework for stability and synchronization analysis of networks of infinite-dimensional linear systems