Abstract

We have shown in previous work that the synchronization of networks of identical finite-dimensional linear systems can be characterized by the stability of the decoupled systems under suitable complex feedback. In this paper we show that this characterization relies on the equivalence of stability and vanishing-input-vanishing-output properties, which is not guaranteed in general for infinite-dimensional systems. This equivalence is established for second-order parabolic PDEs, thus enabling a synchronization analysis similar to its finite-dimensional counterpart.

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