Synchronization of Identical Linear Systems and Diffusive Time-Delayed Couplings

We study the problem of controlled network synchronization for a class of identical linear systems. The systems are interconnected through static and dynamic diffusive couplings with time-delays. In particular, we derive conditions on the systems, on the couplings, on the time-delay, and on the network topology that guarantee global synchronization of the systems. Diffusive time-delayed dynamic couplings are constructed by combining linear observers and output feedback controllers. Using passivity properties, sufficient conditions for boundedness of the interconnected systems are derived. Moreover, predictor-based dynamic couplings are proposed in order to enhance robustness against time-delays in the network. The results are illustrated by numerical simulations.