  Time lags occur in a vast range of real-world dynamical systems due to finite
reaction times or propagation speeds. Here we derive an analytical approach to
determine the asymptotic stability of synchronous states in networks of coupled
inertial oscillators with constant delay. Building on the master stability
formalism, our technique provides necessary and sufficient delay master
stability conditions. We apply it to two classes of potential future power
grids, where processing delays in control dynamics will likely pose a challenge
as renewable energies proliferate. Distinguishing between phase and frequency
delay, our method offers an insight into how bifurcation points depend on the
network topology of these system designs.
