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.

中文翻译：

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惯性振荡器网络的延迟主稳定性

由于有限的反应时间或传播速度，在大量的现实世界动力学系统中会出现时滞。在这里，我们导出一种分析方法来确定具有恒定延迟的耦合惯性振荡器网络中同步状态的渐近稳定性。在主稳定性形式主义的基础上，我们的技术提供了必要和足够的延迟主稳定性条件。我们将其应用于两类潜在的未来电网，随着可再生能源的激增，控制动态中的处理延迟可能会带来挑战。在相位和频率延迟之间进行区分，我们的方法提供了对分叉点如何取决于这些系统设计的网络拓扑的见解。