Minimizing interactions in mixed oscillator networks

This paper investigates the use of a single control node to minimize the interactions in a network of coupled oscillators as it maintains a synchronous state in the face of disturbances. We define an ℋ₂-norm that quantifies these interactions by considering the effect of exogenous disturbances on the relative separation of oscillator phases. Under some simplifying assumptions, we show that a single control node that is directly coupled to every oscillator cannot reduce the total network interactions. Additionally, we analyze the system in the frequency domain to gain insight about the interactions in such a network.