  We consider the problem of controlling the frequency of low-inertia power
systems via inverter-based resources (IBRs) that are weakly connected to the
grid. We propose a novel grid-forming control strategy, the so-called frequency
shaping control, that aims to shape the frequency response of synchronous
generators (SGs) to load perturbations so as to efficiently arrest sudden
frequency drops. Our solution relaxes several existing assumptions in the
literature and is able to navigate tradeoffs between peak power requirements
and maximum frequency deviations. Finally, we analyze the robustness to
imperfect knowledge of network parameters, while particularly highlighting the
importance of accurate estimation of these parameters.
