Why are synchronised linear multi-agent systems sensitive to parameter deviations?

Abstract

The paper investigates the robustness of synchronised linear systems with respect to parameter deviations. It shows that for oscillator networks even infinitesimally small changes of the agent parameters make the overall system to become asymptotically stable and, hence, not synchronisable with respect to a non-trivial synchronous trajectory. This phenomenon raises the question: Why is the property of synchrony so sensitive with respect to the agent parameters? The paper gives an explanation by showing that the synchronous behaviour of any linear multi-agent system appears in a part of the state space that is unobservable by the networked controller. As the overall system is not completely observable but structurally observable, any parameter deviation generally makes the unobservable part to become observable. Hence, this part is moved into the control loop of the networked controller and, for oscillator networks, it gets asymptotically stabilised, which destroys the synchrony of the overall system.